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LIGHT
(c) Quantum Theory of Light :
OPTICS
It is a branch of physics which deals with the study of
light. It is mainly divided into three parts :
(a) Geometrical optics or ray optics :
It deals with the reflection and refraction of light.
(b) Wave or physical optics :
It is concerned with nature of light and deals with
interference, diffraction and polarisation.
According to ‘Planck’ light travels in the form of energy
packets or quantas of energy called photons.
The rest mass of photon is zero. Each quanta carries
energy E = h.
h  Planck’s constant = 6.6 × 10–34 J-s.
  frequency of light
Some phenomenons like interference of light,
diffraction of light are explained with the help of wave
theory but wave theory was failed to explain the photo
electric effect of light. It was explained with the help of
quantum theory. So, light has dual nature.
(c) Quantum optics :
It deals with the interaction of light with the atomic
entities of matter such as photo electric effect, atomic
excitation etc.
Light is the invisible form of energy that causes the
sensation of vision. Light waves are electromagnetic
waves.
De Broglie explaind the dual nature of light, i,e,wave
nature and particle nature.
(i) wave nature : Light is a electromagnetic waves it is
transverse in nature and propagate in vacuum
(ii) Particle or Photon Nature : With the help of this
theory Einstein explained the photo electric effect.
REFLECTION OF LIGHT
(a) Definitions of Reflection :
Theories about nature of light :
Light
(Newton’s
According to Newton light travels in space with a great
speed as a stream of very small particles called
corpuscles.
(b) General definitions about Reflection :
(i) Mirror :
A smooth polished surface from which regular reflection
can take place is called mirror. MM’ is the mirror as
shown in figure.
N
Ang
nt
id e n
Gla
of nce
inc an
ide gle
nc
e
Mirror
M
ce
Photoelectric effect was not explained with the help of
wave theory, so Plank gave a new theory which was
known as quantum theory of light.
This theory is failed to explain photo electric effect.
ra y
Huygen consider the light remains in the form of
mechanical rays and he consider a hypothetical
medium like ether for propagation of light waves.
So, light waves are decleared electromagnetic waves
so there is no need of medium for the propagation of
these waves. They can travel in vacuum also. The speed
of these waves in air or in vacuum is maximum i.e., 3 ×
108 m/s.
f in c
le o
id e
(b) Wave Nature of Light :
C
N orm al
A
In c
According to this theory reflection and refraction of light
are explained while this theory was failed to explain
interference of light and diffraction of light. So wave
theory of light was discovered.
The phenomena of bouncing back of light in same
medium after striking at the interface of two media is
called reflection of light.
i
r
Ang
le o
f re f
Gl
le c t
o f anc
io n
re f e
a
le c n R
t io g le e f le
n
c te
dr
ay
NATURE OF LIGHT
(a) Particle Nature of
corpuscular theory) :
( d ) Dual Nature of Light :
Reflecting surface
M'
B
Terms associated with reflection
(a) Laws of Reflection :
The reflection of light from a surface obeys certain laws
called laws of reflection. They are:
NTSE STAGE-I_PAGE # 1
Regular reflection takes place from the objects like looking
glass, still water, oil, highly polished metals, etc.
Regular reflection is useful in the formation of images,
e.g., we can see our face in a mirror only on account of
regular reflection. However, it causes a very strong glare
in our eyes.
Irregular reflection or Diffused reflection :
(i) Angle of Incidence is equal to the angle of reflection,
i.e., i = r.
(ii) Incident ray, reflected ray and normal to the reflecting
surface always lie in the same plane.
Important Information :
(i) A ray of light striking the surface normally retraces its
path.
Irregular or diffused reflection
The phenomenon due to which a parallel beam of light,
travelling through some medium, gets reflected in
various possible directions, on striking some rough
surface is called irregular reflection or diffused
reflection.
(ii) Laws of reflection are also obeyed when light is
reflected from the spherical or curved surfaces as
shown in figure (a) and (b)
I
N
R
I
N
i r
i r
(a)
(b)
The reflection which takes places from ground, walls,
trees, suspended particles in air, and a variety of other
objects, which are not very smooth, is irregular
reflection.
Irregular reflection helps in spreading light energy over
a vast region and also decreases its intensity. Thus, it
helps in the general illumination of places and helps
us to see things around us.
R

Reflection from curved surface
(C ) Regular and Irregular Reflection :
Regular reflection :
The phenomenon due to which a parallel beam of light
travelling through a certain medium, on striking some
smooth polished surface, bounces off from it, as
parallel beam, in some other fixed direction is called
Regular reflection.
NOTE : Laws of reflection are always valid no matter
whether reflection is regular or irregular.
RECTILINEAR PROPAGATION OF LIGHT
Definition :
In simplest terms, rectilinear propagation of light
means that light energy travels in straight lines.
Examples of rectilinear propagation of light in
everyday life :
(i) When the sunlight enters through a small hole in a
dark room, it appears to travel in straight lines.
(ii) The light emitted by the head light of a scooter at
night appears to travel in straight lines.
(iii) If we almost close our eyes and try to look towards
a lighted bulb, it appears to give light in the form of
straight lines, which travel in various direction.
Experiment to prove rectilinear propagation of light:
Regular reflection
Take three wooden upright A, B and C having a small
hole in the middle, such that the holes are at the same
height from the base. Arrange the uprights along the
edge of a table, such that holes are in the same straight
NTSE STAGE-I_PAGE # 2
line. Place a lighted candle towards the upright A, such
that it is facing the hole. Look through the hole of upright
C. The candle flame is clearly visible.
A
N
C
1
A
B
C
M
D
r
i
3
M'
B
4
2
A'
from the above diagram :
Illustrating rectilinear propagation of light
Now displace upright B, slightly towards right or left. It
is seen that candle flame is no longer visible. This
shows that light travels in straight lines.
.......(i)
i  1
.......(ii)
(alternate interior angles)
2  r
.......(iii)
(corresponding angles)
(law of reflection)
 From equation (i), (ii) and (iii) 1  2 .......(iv)
In BA ' A, 1  2  AB  A ' B
Definition :
In BDA and BDA
AB = AB (proved above), BD is common and 3 = 4
(each 90º)
An optical image is a point where rays of light converge
actually or appear to diverge. The image of an extended
object is an assembly of image points corresponding
to various points on the object.
  ADB  A ' DB (By RHS rule)  AD = A ' D
So the image of an object formed by the plane mirror is
at same distance behind the plane mirror as the object
is in front of it.
Real image :
(b) Characteristics of Image Formed by a
Plane Mirror :
IMAGE
If the rays of light after reflection (or refraction) converge
actually at a point then the image formed is called real
image. It can be seen as well as obtained on a screen
placed at the position of the image.
Virtual image :

i  r
(i) It is of the same size as that of the object.
(ii) It is at same distance behind the mirror as the object
is in front of it.
(iii) It is laterally inverted.
If the rays of light don’t converge actually but appear to
diverge from a point then the image formed is called
virtual image. It cannot be taken on screen.
Both the real and virtual image can be photographed.
(iv) It is virtual and erect.
 Points to Remember :
(i) Focal length of a plane mirror is infinity.
Real Image
Virtual Image
1. A real image is formed when 1. A virtual image is formed
two or more reflected rays meet at when two or more rays appear to
a point in front of the mirror.
be coming from a point behind
the mirror.
(ii) Power of a plane mirrors is zero.
2. A real image can be obtained
on a screen.
2. A virtual image cannot be
obtained on a screen.
tated through an angle , about an axis in the plane of
3. A real image is inverted with
respect to the object.
3. A virtual image is erect with
respect to the object.
(iii) If keeping the incident ray fixed, the mirror is romirror, the reflected ray is rotated through an angle 2
M
M
Incident ray
Incident ray
Reflected ray
PLANE MIRROR
(a) Image Formed by a Plane Mirror :
M'
Reflected ray
The image of an object A is formed at Awith the help of
plane mirror (MM)
NTSE STAGE-I_PAGE # 3
M'
(iv) As every part of a mirror forms a complete image
of an extended object and due to super-position of
images brightness will depend on its light reflecting
area, a large mirror gives more bright image than a
small one. This in turn also implies that if a portion of
a mirror is obstructed, complete image will be formed
but of reduced brightness.
(v) Though every part of a mirror forms a complete
image of an object, we usually see only that part of it
from which light after reflection from the mirror reaches
our eye. That is why :
(A) To see his full image in a plane mirror a person
requires a mirror of at least half of his height.
(B) To see a complete wall behind himself a person
requires a mirror of at least (1/3rd) the height of wall
and he must be in the middle of wall and mirror.
(vi) Deviation  is defined as the angle between directions of incident ray and emergent ray.
 = 180 – (i + r) = 180 – 2i
(d) Number of Images formed when the object
is placed between Two Plane Mirrors :
When two plane mirrors are placed facing each other
at an angle  and an object is placed between them,
multiple images are formed as a result of multiple
reflections.
If
360º
is even then the number of image formed,

n=
r
i
If
Plane mirror
(vii) If an object moves towards (or away from) a plane
mirror at speed v, the image will also approach (or
recede) at same speed v i.e., the speed of image relative to object will be 2v.
360º
– 1.

360º
is odd then :

Case I :
n=
360º
– 1.

Case II :
n=
But the amplitude or intensity of the reflected ray is
less than that of the incident ray.
Case III : If
(x) If angle between two mirrors is  then after two
consecutive reflection
total deviation 
= 1 + 2 = 2 – 2
(xi) A thick plane mirror forms number of images, due
to multiple reflection of light. Out of these images, second image is the brightest and the intensity of other
images goes on decreasing.
If the object lies asymmetrically, then
360º
.

(viii)In reflection the speed, wavelength and frequency
of light does not change.
(ix) Plane mirrors are used in sextant, Kaleidoscope,
Periscope
If the object lies symmetrically, then
360º
is equal to fraction then number of

images=[n] i.e. only integer part.
SPHERICAL MIRROR
A mirror whose reflecting surface is a part of a hollow
sphere of glass is known as spherical mirror. For
example, a dentist uses a curved mirror to examine
the teeth closely, large curved mirrors are used in
telescopes .These are of two types convex and concave.
In concave mirror, reflecting surface is concave but in
convex mirror, reflecting surface is convex.
(c) Lateral Inversion :
Letter L appears to be inverted or reversed, i.e. there is
an interchange of left and right sides of the image and
the object.
Eg. : If a man stands in front of a plane mirror his right
hand appears to be the left hand of the image.
Convex Mirror
NTSE STAGE-I_PAGE # 4
Concave Mirror
(a) Some terms related to spherical mirror :
(vii) Focal length : The distance between the pole and
the focus is called the focal length. The focal length is
half the radius of curvature.
Light gets reflected from
concave surface
Principal
axis
(viii)Focal plane : A plane passing through the principal
focus and at right angles to the principal axis of a
spherical mirror is called the focal plane.
Silver coating
Pole
( P)
Aperture
C
Light reflect
from convex
surface
Centre of curvature
Radius of curvature
Concave mirror
Aperture
Principal
axis
C
Centre of curvature
CONCAVE AND CONVEX MIRROR
Radius of curvature
Convex mirror is a spherical mirror, whose inner (cave
Convex mirror
(i) Pole : The central point of a mirror is called its pole.
type) surface is silvered and reflection takes place at
the outer (convex) surface.
(ii) Centre of curvature : The centre of the sphere of
which the mirror is a part is called centre of
curvature.
Concave mirror is a spherical mirror, whose outer
bulged surface is silvered and reflection takes place
from the inner hollow (cave type) surface.
(iii) Radius of curvature : The radius of the sphere of
which the mirror is a part is called radius of curvature.
(a) Rules for the formation of images by
(iv) Principal axis : The straight line joining the pole
and the centre of curvature is called the principal axis.
concave and convex mirrors :
(v) Aperture : The size of the mirror is called its
aperture.
passes (concave) or appears to pass (convex) through
the focus.
(i) A ray incident parallel to the principal axis actually
(vi) Principal focus :
Focus of concave
mirror
A parallel beam of light
after reflection from a
concave mirror converges
at a point in front of the
mirror. This point (F) is
the focus of a concave
mirror and it is real.
Focus of
convex mirror
A parallel beam of light after
reflection from a convex
surface diverges and the rays
do not meet. However on
producing backward, the rays
appear to meet at a point
behind the mirror. This point is
focus of the convex mirror and
it is virtual.
P
F
C
(a)
(ii) A ray incident through the centre of curvature (C)
falls normally and is reflected back along the same
path.
F
C
P
P
F
C
(c)
(iii) A ray incident through the focus is reflected parallel
to the principal axis.
NTSE STAGE-I_PAGE # 5
solar cookers : When a parallel beam of sunlight falls
on a concave mirror, this beam is brought to the focus
of the mirror (see figure). As a result of this, the
temperature of an object (say a container containing
uncooked food) placed at the focus increases
considerably. Hence the food in the container is
cooked.
(b) Image formed by convex mirror : The
position, size and nature of the image formed by a
convex mirror depends upon the distance of the
object from the pole of the mirror. For a convex
mirror, the position and nature of image formed is
summerised in the table :
Position of
the object
Position of
the image
At infinity
At F
Between
O and 
Between
O and F
Size of
the image
Container
containing
food
Nature of
the image
Spherical Reflector type solar cooker
Highly diminished Virtual and erect
Diminished
Virtual and erect
SIGN CONVENTION FOR MEASURING DISTANCE
IN CONCAVE AND CONVEX MIRROR
(i) All distances are measured from the pole.
USES OF CONVEX MIRROR
(ii) The incident ray is taken from left to right.
Convex mirror is used as rear view mirror in automobiles
like cars, trucks and buses to see the traffic at the back
side. It is also used in street lamps.
(iii) Distances measured in the same direction as that
of the incident ray are taken to be +ve.
(iv) Distances measured in a direction opposite to the
incident ray are taken to be –ve.
(a) Image formed by concave mirror:
The position, size and nature of the image formed by a
(v) Distances measured upwards and perpendicular
to principal axis are taken +ve.
concave mirror depends upon the distance of the object
from the pole of the mirror. For a concave mirror, the
position and nature of image formed is summerised
in the table :
Position of
Object
At infinity
Position of
Image
At focus F
Size of
Image
Highly diminished
Nature of
Image
Real and inverted
Beyond C
Between F and C Diminished
Real and inverted
At C
At C
Same size
Real and inverted
Between F and C Beyond C
Enlarged
Real and inverted
At F
At infinity
Highly enlarged
Real and inverted
Between P and F
Behind the mirror Enlarged
(vi) Distances measured downwards and perpendicular
to principal axis are taken –ve.
Incident
Light
Incident
Light
A
B
A
C
B'
F
P
B
A'
P
B' F
C
A'
(a)
(b)
Virtual and erect
(b) Uses of concave mirror :
(i) They are used as shaving mirrors.
(iii) They are used by doctors to concentrate light on
body parts like ears and eyes which are to be examined.
Focal length of concave mirror is – ve 
 ocal length of conve mirror is ve 
x
F



 For real image v is  ve

for virtual image v is  ve

(iv) Large concave mirrors are used in the field of solar
energy to focus sun-rays on the objects to be heated.
IMPORTANT : These signs are according to the rectilinear
co-ordinate system.
(ii) They are used as reflectors in car head-lights, search
lights, torches and table lamps.
NTSE STAGE-I_PAGE # 6
of its path changes at the interface of the two media.
This is called refraction of light.
MIRROR FORMULA
The mirror formula is a relation relating the object
distance (u), the image distance (v) and the focal length
(f) of a mirror.
The mirror formula is :
1
1
1
+
=
u
v
f
above equation is known as mirror formula and is valid
for both concave and convex mirrors. However, the
quantities must be substituted with proper signs.
The phenomenon of the change in the path of the light
as it passes from one transparent medium to another
is called refraction of light. The path along which the
light travels in the first medium is called incident ray
and that in the second medium is called refracted ray.
The angles which the incident ray and the refracted ray
make with the normal at the surface of separation are
called angle of incidence (i) and angle of refraction (r)
respectively.
POWER OF MIRROR
A spherical mirror has infinite number of focus. Optical
power of a mirror (in Diopters) = –
1
f (in metre)
MAGNIFICATION OF CONCAVE MIRROR
The linear magnification of a spherical mirror is the
ratio of height of the image (h2) formed by the mirror to
the height of the object (h1) i.e.
Linear magnification, m =
Height of image
h2
Height of object = h
1
The linear magnification is a number that simply tells
us how much taller the image is than the object. For
example, if m = 1, it means that the image and the
object are of the same height.
Another formula for magnification is :
m=–
f
v
=
f u
u
The arbitrary minus sign given to linear magnification
has nothing to do with the relative sizes of the object
and the image but we can use it to tell whether the
image is erect or inverted w.r.t. object.
Incident ray
Normal
NOTE: Always draw a rough ray diagram while solving
a numerical problem. Otherwise we will be confused
as to which distance should be taken as +ve & which –
ve.
For virtual image : m is +ve [as virtual image is erect
 h2 is +ve as well as h1 is +ve]
For real image : m is –ve [as real image is always
inverted  h2 is –ve while h1 is +ve]
Air
Glass
(C)
Refracted
ray
Showing different cases of refraction
It is observed that :
ILLUSTRATIONS
(i) When a ray of light passes from an optically rarer
medium to a denser medium, it bends towards the
normal (r < i ), as shown in figure (A).
REFRACTION OF LIGHT
(ii) When a ray of light passes from an optically denser
to a rarer medium, it bends away from the normal
(r > i) as shown in figure (B) .
When light travels in the same homogeneous medium,
it travels along a straight path. However, when it passes
from one transparent medium to another, the direction
(iii) A ray of light travelling along the normal passes
NTSE STAGE-I_PAGE # 7
eye
undeflected, as shown in figure (C). Here i = r = 0°.
(a) Cause of Refraction :
We come across many media like air, glass, water etc.
A medium is a transparent material through which light
is transmitted. Every transparent medium has a
property known as optical density. The optical density
of a transparent medium is closely related to the speed
of light in the medium. If the optical density of a
transparent medium is low, then the speed of light in
that medium is high. Such a medium is known as
optically rarer medium. Thus, optically rarer medium
is that medium through which light travels fast. In other
words, a medium in which speed of light is more is
known as optically rarer medium.
air
B
Q
(ii) A water tank appears shallow i.e. less deep than
its actual depth :
On the other hand, if the optical density of a transparent
medium is high, then the speed of light in that medium
is low. Such a medium is known as optically denser
medium. Thus, optically denser medium is that
medium through which light travels slow. In other
words, a medium in which speed of light is less is
known as optically denser medium.
Speed of light in air is more than the speed of light in
water, so air is optically rarer medium as compared to
the water. In other words, water is optically denser
medium as compared to air. Similarly, speed of light in
water is more than the speed of light in glass, so water
is optically rarer medium as compared to the glass. In
other words, glass is optically denser medium as
compared to water.

When light goes from air (optically rarer medium) to
glass (optically denser medium) such that the light in
air makes an angle with the normal to the interface
separating air and glass, then it bends from its original
direction of propagation. Similarly, if light goes from
glass to air, again it bends from its original direction of
propagation. The phenomena of bending of light from
its path is known as refraction. We have seen that the
speed of light in different media is different, so we can
say that refraction of light takes place because the
speed of light is different in different media. Thus, the
cause of refraction can be summarised as follows :
NOTE :
(i) Refraction is the deviation of light when it crosses
the boundary between two different media (of different
optical densities) and there is a change in both
wavelength and speed of light.
(ii) The frequency of the refracted ray remains unchanged.
(iii) The intensity of the refracted ray is less than that
of the incident ray. It is because there is partial reflection
and absorption of light at the interface.
(b) Effects of refraction of Light :
(i) A pencil appears bent and short in water :
water
C
A
B
I
O
(iii) Apparent shift in the position of the sun at sunrise and sunset
Due to the atmospheric refraction, the sun is visible
before actual sunrise and after actual sunset.
S
Apparent
Position
of Sun
Atmosphere
Horizon
Observer
S
Actual
Position
of Sun
Earth
Refraction effect at sunset and sunrise
With altitude, the density and hence refractive index of
air-layers decreases. The light rays starting from the
sun S travel from rarer to denser layers. They bend
more and more towards the normal. However, an observer sees an object in the direction of the rays reaching his eyes. So to an observer standing on the earth,
the sun which is actually in a position below the horizon, appears in the position S’, above the horizon. The
apparent shift in the position of the sun is by about
0.5 0. Thus the sun appears to rise early by about
2 minutes and for the same reason, it appears to set
late by about 2 minutes. This increases the length of
the day by about 4 minutes.
(iv) Twinkling of stars :
On a clear night, you might have observed the twinkling
of a star, which is due to an atmospheric refraction of
NTSE STAGE-I_PAGE # 8
star light. The density of the atmosphere, as we know
goes on decreasing as the distance above the sea
level increases. For the sake of simplicity, air can be
supposed to be made up of a very large number of
layers whose density decreases with the distance
above the surface of the earth. Therefore, the light from
a heavenly body, such as a star, goes on gradually
bending towards normal as it travels through the
earth’s atmosphere. As the object is always seen in
the direction of the light reaching the observer’s eye,
the star appears higher up in the sky than its actual
position. Further, the densities of the various layers go
on varying due to the convection currents set up in air
by temperature differences. Thus, the refractive index
of a layer of air at a particular level goes on changing.
Due to these variations in the refractive indices of the
various layers of air, the light from a star passing through
the atmospheric air changes its path from time to time
and therefore, the amount of light reaching the eye is
not always the same. This increase or decrease in the
intensity of light reaching the eye results in the change
in apparent position or twinkling of the star.
(b) Refractive ndex in terms of Wavelength :
Since the frequency
 
remains unchanged when
light passes from one medium to another, therefore,

 vac
c  vac  
=
=
 med
v  med  
The refractive index of a medium may be defined as
the ratio of wavelength of light in vacuum to its
wavelength in that medium.
(c) Relative Refractive ndex :
The relative refractive index of medium 2 with respect
to medium 1 is defined as the ratio of speed of light
(v1) in the medium 1 to the speed of light (v2) in medium
2 and is denoted by 1 2 .
Thus,
1 2
=
1
v1
=
v2
2
=
2
1
As refractive index is the ratio of two similar physical
quantities, so it has no unit and dimension.
(c) Laws of Refraction :
There are two laws of refraction :
Factors on which the refractive index of a medium
depends are :
(i) The incident ray, the refracted ray and the normal at
the point of incidence lie in the same plane.
(i) Nature of the medium.
sin i
(ii)
= constant called refractive index denoted
sin r
by ‘  ’.
(ii) Wavelength of the light used.
The above law is called snell’s law (Willibrod Snell).
(iv) Nature of the surrounding medium.
Eg.
(iii) Temperature.
sin i
= 1 2
sin r
Here
1 2
It may be noted that refractive index is a characteristic
of the pair of the media and also depends on the
wavelength of light, but is independent of the angle of
incidence.
Physical significance of refractive index :
is called refractive index of 2nd medium
w.r.t. 1st medium.
Laws of refraction are valid for both types of surfaces 


i.e. for plane as well as spherical refracting surfaces. 
The refractive index of a medium gives the following
two informations :
(i) The value of refractive index gives information about
the direction of bending of refracted ray. It tells whether
the ray will bend towards or away from the normal.
REFRACTIVE INDEX
(a) Refractive ndex in terms of Speed of
Light :
(ii) The refractive index of a medium is related to the
speed of light. It is the ratio of the speed of light in vacuum
to that in the given medium. For example, refractive index
of glass is 3/2. This indicates that the ratio of the speed
of light in glass to that in vacuum is 2 : 3 or the speed of
light in glass is two-third of its speed in vacuum.
The refractive index of a medium may be defined in
terms of the speed of light as follows :
The refractive index of a medium for a light of given
wavelength may be defined as the ratio of the speed of
light in vacuum to its speed in that medium.
Speed of light i n vacuum
Refractive index = Speed of light in medium
or

c
v
5.
A ray of light AO is incident on the surface of oil. Reflected
part of this ray OB and refracted part OC are mutually
perpendicular as shown. Find refractive index of oil.
Refractive index of a medium with respect to vacuum
is also called absolute refractive index.
NTSE STAGE-I_PAGE # 9
T
A
 In QOP sin i = sin OPQ 
60º
Air
Oil
Sol..
B
O
a ìw
=
OQ/P' Q PQ

OQ/PQ P' Q
.......... (4)
Nearly normal direction of viewing angle i is very small
PQ  PO and P’Q  P’O
 from (4)
60º 60º
30º
O
30º
C
sin 60 º
3 /2
=
=
=
sin 30 º
1/ 2
.......... (3)
So, from (1),(2) and (3)
C
B
sin i A
µ=
sin r
OQ
PQ
a ìw
3
=
PO

P' O
a ìw
=
Real depth
Apparent depth
REFRACTION THROUGH GLASS SLAB
(d) Refractive ndex in terms of apparent
depth and real depth :
Whenever we observe the bottom of a swimming pool
or a tank of clear water, we find that the bottom appears
to be raised i.e. the apparent depth is less as compared
to its real depth.
The extent to which the bottom appears to be raised
depends upon the value of refractive index of the refracting
medium.
(a) Refraction through a rectangular glass
slab and principle of reversibility of light :
Consider a rectangular glass slab, as shown in figure.
A ray AE is incident on the face PQ at an angle of
incidence i . On entering the glass slab, it bends
towards normal and travels along EF at an angle of
refraction r. The refracted ray EF is incident on face FR
at an angle of incidence r. The emergent ray FD bends
away from the normal at an angle of refraction e.
Thus the emergent ray FD is parallel to the incident ray
AE, but it has been laterally displaced with respect to
the incident ray. There is shift in the path of light on
emerging from a refracting medium with parallel faces.
Lateral shift :
Eye
R
N
N1
r
Q
rarer medium
(medium 1)
O
apparent
depth
T
r
Lateral shift is the perpendicular distance between the
incident and emergent rays when light is incident
obliquely on a rectangular slab with parallel faces.
Factors on which lateral shift depends are :
i N2
real depth
i
denser medium
(medium 2)
(i) Lateral shift is directly proportional to the thickness
of glass slab.
(ii) Lateral shift is directly proportional to the incident
angle.
(iii) Lateral shift is directly proportional to the refractive
index of glass slab.
P
(iv) Lateral shift is inversely proportional to the
wavelength of incident light.
In above fig. PQN2  i & N1QR  r
 w ìa =
sin i
sin r
or a ì w =
sin r
sin i
.......... (1)
As N1QR  OPQ  r
(corresponding angles)
In OP Q
sin r = sin OP' Q 
OQ
.......... (2)
P' Q
and i  PQN 2  QPO (alt. Int. ( s))
If a plane mirror is placed in the path of emergent ray
NTSE STAGE-I_PAGE # 10
FD then the path of the emergent ray along FD is
reversed back, it follows the same path along which it
was incident i.e. the incidence ray becomes the
emergent ray & emergent ray becomes the incident
ray. It is known as principle of reversibility of light.
Case-I : For light going from air to water .
i = angle of incidence, r = angle of refraction.
a ìg
=
sin i
sin r
.......................(1)
( a ì g = absolute refractive index of glass)
Case-II : For light going from glass to air at point F.
Different types of convex lens
sinr
 g ìa = sine
(b) Concave lens and its types :
 r   angle of incidence 
  r  r
where 
 e  angle of refraction 
 g ìa =
sin r
sin i
(as e  i )
A lens which is thin at the middle and thick at the edges
is called a concave lens. The most common form of a
concave lens has both the surfaces depressed inward
at the middle. Some forms of concave lenses are
shown in the figure.
sin i
1
 ì  sin r .......................(2)
g a
 From (1) & (2)
e  i , hence incident ray and emergent ray are
parallel.
a ìg =
1
g ìa

a  g g a
1
Different types of concave lens
SPHERICAL LENSES
(c) Definitions in connection with spherical
lens :
Optical
Centre
A lens is a piece of transparent refracting material
bounded by two spherical surfaces or one spherical
and other plane surface.
A lens is the most important optical component used
in microscopes, telescopes, cameras, projectors etc.
Basically lenses are of two types :
(i) Convex lens or converging lens
Radius of
Curvature
Centre of
Curvature
C2
R1
P1
P2
R2
O
C1
Principal
axis
(a)
(ii) Concave lens or diverging lens
(a) Convex lens and its types:
A lens which is thick at the centre and thin at the edges
is called a convex lens. The most common form of a
convex lens has both the surfaces bulging out at the
middle. Some forms of convex lens are shown in the
figure.
Figure : Characteristics of convex and concave
NTSE STAGE-I_PAGE # 11
lenses
(i) Optical centre :
If a ray of light is incident on a lens such that after
refraction through the lens the emergent ray is parallel
to the incident ray, then the point at which the refracted
ray intersects, the principal axis is called the optical
centre of the lens. In the figure O is the optical centre of
the lens. It divides the thickness of the lens in the ratio
of the radii of curvature of its two surfaces.
If the radii of curvature of the two surfaces are equal
then the optical centre coincides with the geometric
centre of the lens.
O
f
Figure : Ray diagram showing First principal focus
(B) Second principal focus and second focal length :
It is a fixed point on the principal axis such that the light
rays incident parallel to the principal axis, after refraction
through the lens, either converge to this point (in convex
lens) or appear to diverge from this point (in concave
lens). The plane passing through this point and
perpendicular to principal axis is called the second
focal plane. The distance between the second principal
focus and the optical centre is called the second focal
length. It is denoted by f2 or f.
(b)
Figure : Ray diagram showing Second principal
focus
For a ray passing through the optical centre, the
incident and emergent rays are parallel. However, the
emergent ray suffers some lateral displacement
relative to the incident ray. The lateral displacement
decreases with the decrease in thickness of the lens.
Hence a ray passing through the optical centre of a
thin lens does not suffer any lateral deviation, as shown
in the figure above.
(ii) Principal foci and focal length :
(A) First principal focus and first focal length :
It is a fixed point on the principal axis such that rays
starting from this point (in convex lens) or appearing to
go towards this point (concave lens), after refraction
through the lens, become parallel to the principal axis. It
is represented by F1 or f. The plane passing through
this point and perpendicular to the principal axis is called
the first focal plane. The distance between first principal
focus and the optical centre is called the first focal length.
It is denoted by f1 or f.
Generally, the focal length of a lens refers to its second
focal length. It is obvious from the above figures, that
the foci of a convex lens are real and those of a concave
lens are virtual. Thus the focal length of a convex lens
is taken positive and the focal length of a concave lens
is taken negative.
If the medium on both sides of a lens is same, then
the numerical values of the first and second focal
lengths are equal. Thus
f = f
CONVEX LENS
(a) Rules for image formation by Convex
Lens :
The position of the image formed by a convex lens can
be found by considering two of the following rays (as
explained below).
(i) A ray of light coming parallel to principal axis, after
refraction through the lens, passes through the
principal focus (F) as shown in the figure.
NTSE STAGE-I_PAGE # 12
CONCAVE LENS
(a) Rules for image formation by Concave
Lens :
O
The position of the image formed by a concave lens
can be found by considering following two rays coming
from a point object (as explained below).
F
(i) A ray of light coming parallel to the principal axis,
after refraction, appears to pass through the principal
focus F of the lens, when produced backward as shown
in figure (a) .
Convex Lens
(ii) A ray of light passing through the optical centre O
of the lens goes straight without suffering any deviation
as shown in the figure.
(ii) A ray of light passing through the optical centre O of
the lens goes straight without suffering any deviation as
shown in figure (b).
F
O
F
(iii) A ray of light coming from the object and passing
through the principal focus of the lens after refraction
through the lens, becomes parallel to the principal axis.
(b)
(a)
(b) Image formed by Concave Lens :
F
The image formed by a concave lens is always virtual,
erect and diminished and is formed between the optical
centre O and the principal focus F of the lens. For a thin
concave lens of small aperture, the position and nature
of image formed is summerised in the table :
O
(b) Image formed by Convex Lens :
The position, size and nature of the image formed by a
convex lens depends upon the distance of the object
from the optical centre of the lens. For a thin convex
lens, the position and nature of image formed is
summerised in the table :
Position of
the object
At infinity
Position of
the image
Size of
the image
At the focus F Highly diminished
Nature of
the image
Position of
the object
Position of
the image
At infinity
At F
Between
O and 
Between
O and F

Size of
the image
Nature of
the image
Highly diminished Virtual and erect
Diminished
Virtual and erect
POWER OF A LENS
Real and inverted
Beyond 2F
Between
F and 2F
Diminished
Real and inverted
It is the measure of deviation produce by a lens. It is
defined as the reciprocal of its focal length in metres.
At 2F
At 2F
Same size
Real and inverted
Its unit is Diopter (D) (f should always be in metres).
Between
F and 2F
Beyond 2F
Magnified
Real and inverted
At F
At infinity
Highly magnified
Real and inverted
Between
O and F
On the side of
the object
Magnified
Virtual and erect
Power (P) =
1
focal length( f in m)
NTSE STAGE-I_PAGE # 13
Power of a convex lens is +ve (As it has a real focus
and its focal length measured is +ve.)
Power of a concave lens is –ve (As it has a virtual focus
The angle A included between the two refracting faces
is called angle of the prism.
Refracting
edge
and its focal length measured is –ve.)

NOTE :
If two thin lenses are placed in contact, the combination
has a power equal to the algebraic sum of the powers
of two lenses, P = P1 + P2

1 1 1.
 
f f1 f2
Principal
section
Refracting
A
faces
Angle
of prism
B
A
D
E
F
C
B
C
Any section of the prism cut by a plane perpendicular
to the refracting edge is called principal section of the
prism.
Here, f1 and f2 are the focal length of lenses and f is
focal length of combination of lenses.
(b) Determination of angle of deviation :
Let abc be the principal section of a prism of refracting
angle A. Let a light ray AB be incident on the refracting
surface ab of the prism at an angle i. After refraction at
LENS FORMULA
Relation between object distance u, image distance v
and focal length f is :
1 1 1
  .
v u f
B, the ray of light bends towards the normal NO and
travels along BC. The refracted ray BC again suffers a
refraction at C and bends away from the normal N’O
and travels along CD. The ray CD is called emergent
ray. The angle made by the emergent ray with the normal
is called angle of emergence (i.e. e). When the
NOTE : Lens maker formula :
emergent ray is produced backward, it meets the
incident ray produced forward at point M. The angle
1 (  1)  1  1    lens  1  1  1 
=
R R  
 R R 
F
2
2 
 1
 medium
 1
between the emergent ray and the incident ray is called
angle of deviation. ().
(where is absolute refractive index of lens material)
LINEAR MAGNIFICATION
Linear magnification (m) is defined as the ratio of the
size of the image to the size of the object.
m
A' B' h 2 height of image


AB
h1 height of object ,
also m 
v
u
if m is  ve (image is virtual & erect.)
Deviation of light through prism
if m is  ve (image is real & inverted)
Angle of deviation is the angle through which incident
REFRACTION THROUGH PRISM
ray is turned by the prism while passing through it. In
other words, the angle between the emergent ray and
(a) Prism :
A prism is a wedge shaped portion of a transparent
refracting medium bounded by two plane faces inclined
to each other at a certain angle. In the following figure.
the direction of incident ray is called angle of deviation.
The two plane faces (ABED and ACFD) inclined to each
other are called refracting faces of the prism.
than the refractive index of the medium of its
surrounding, the emergent ray may bend away from
The line (AD) along which the two refracting faces meet
is called the refracting edge of the prism.
the base of the prism as shown in the figure.
Angle of deviation  = I + e – A
Note : If refractive index of the material of prism is less
The third face (BCFE) of the prism opposite to the refracting edge is called the base of the prism.
NTSE STAGE-I_PAGE # 14
the eye. Similarly if a green leaf is seen in red light, it
appears black.
(v) If a white flower is seen in red light, it appear red
because a white object reflects light of all colours falling
on it. So it reflects the red light falling on it, which then
enters the eye.
denser
denser
The phenomenon of splitting of white light into its
constituent colours is known as dispersion of light.
rarer
It is discovered by Newton.
Colour
Violet
Indigo
Blue
Green
Yellow
Orange
Red
Factors on which angle of deviation depends
(i) The angle of incidence
(ii) The material of the prism
(iii) The wavelength of light used
(iv) The angle of the prism.
Frequency in 10
6.73 – 7.5
6.47 – 6.73
6.01 – 6.47
5.19 – 6.0
5.07 – 5.19
4.84 – 5.07
3.75 – 4.84
14
Hz
Wavelength (nearly)
4000 Å to 4460 Å
4460 Å to 4640 Å
4640 Å to 5000 Å
5000 Å to 5780 Å
5780 Å to 5920 Å
5920 Å to 6200 Å
6200 Å to 8000 Å
(c) Dispersion of Light through a Prism :
Dispersion takes place because light of different
colours have different speed in a medium. Therefore
the refractive index of glass is different for different
colours of light. When white light is incident on the first
A
surface of a prism and enters it, light of different colours
is refracted or deviated through different angles. Thus
m
Be a
h it e
of w
t
ligh
the dispersion or splitting of white light into its
I
V
R
O
Y
G
B
constituent colours takes place.
NOTE: From the definition of refractive index
glass =
speed of light in air
speed of light in glass
Colour of Objects in White and Coloured
Light :
The speed of light for different colours is different in
We known that white light is a mixture of seven colours.
Light can be of different colours. Let us understand
that why different objects appear to have different
colours. A rose appear red because when white light
falls on rose, it reflects only the red component and
absorbs the other components.
We conclude that the colour of an object depends upon
the colour of light it reflects.
and the speed of red light is maximum. Therefore
NOTE :
glass (medium). The speed of violet light is minimum
violet > red
But  = sin i/sin r or sin r = sin i/
Therefore, the angle of refraction is minimum for light
of violet colour and maximum for light of red colour.
Each colour is deviated towards the base of the prism.
The violet is deviated the most and the red is deviated
the least. As a matter of fact, the colours in the spectrum
(i) If an object absorbs lights of all colours and reflects
none, it appears black.
do not have any sharp boundaries.
(ii) If an object reflects light of all colour, it appears
white when seen in white light.
Recombination of the Spectrum :
(iii) When we talk of colour of an object, we refer to its
colour as seen in white light.
material and of the same refracting angle A are arranged
(iv) A rose will appear black in green light because
there is no red component in the light and it will not
reflect any light. Hence no light will come from rose to
the first prism P1 with its base downwards and gets
For this experiment, two prisms P1 and P2 of the same
as shown in figure. Sunlight from a narrow slit S falls on
dispersed into constituent colours (VIBGYOR) and the
bending takes place downwards. Now this dispersed
light falls on the second prism P2 with its base upwards
NTSE STAGE-I_PAGE # 15
enters a smoke filled room through a small hole. Thus,
scattering of light makes the particles visible. Tyndall
effect can also be observed when sunlight passes
through a canopy of a dense forest. Here, tiny water
droplets in the mist scatter light.
so that it deviates the light upwards.
PRISM (P2)
A
ITE
WH T
H
LIG
R
R
v
v
SCREEN
A
PRISM (P1)
It is found that the light coming out of the second prism
P2 is almost white and is in direction parallel to the
direction of light incident on the first prism P1. In fact,
the two prisms P1 and P2 combined together effectively
acts like a parallel sided glass slab. This shows that
the prism P1 simply disperses the white light into its
constituent colours and the prism P2 recombines these
colours to form white light. The prism P1 is called
dispersing-prism and the prism P 2 is known as
recombination-prism.
SCATTERING OF LIGHT
When light falls on tiny particles then diffused reflection
takes place and light spreads in all possible direction.
This phenomenon is known as scattering of light.
Small particles scatter mainly blue light. When size of
the particle increases then the light of longer
wavelength also scatter. The path of a beam of light
passing through a true solution is not visible. However,
its path becomes visible through a colloidal solution
where the size of the particles is relatively larger.
Rayleigh proved that the intensity of scattered light is
inversely proportional to the fourth power of the
wavelength, provided the scatters is smaller in size
than the wavelength of light:
scattering 
1
4
(a) Tyndall Effect :
The earth’s atmosphere is a heterogeneous mixtures
of minute particles. These particles include smoke,
tiny water droplets, suspended particles of dust and
molecules of air. When a beam of light strikes such
fine particles, the path of the beam becomes visible.
The light reaches us after being reflected diffusely by
these particles. The phenomenon of scattering of light
by the colloidal particle gives rise to tyndall effect. This
phenomenon is seen when a fine beam of sunlight
(b) Phenomena based upon Scattering of
Light :
A number of optical phenomena can be explained on
the basis of scattering of light :
(i) Colour of the clear sky is blue : When we look at the
sky, we receive sunlight scattered by fine dust particles,
air molecules and water-vapour molecules present in
the atmosphere. Since blue light, which is present in
larger proportion than violet light in the sunlight, is
scattered about ten times more than the orange-red
light, the light reaching the eye is mainly blue. Hence
the sky appears bluish.
If the earth had no atmosphere, there were no scattered
sunlight and the sky would have appeared black. In
fact, the sky does appear black to the astronauts in the
space above the earth's atmosphere.
(ii) The clouds appears white:- The dependence of
scattering on 1/4 is valid only when the scatterer
particles or molecules are much smaller than the
wavelength of light, as are air molecules. Clouds,
however, contain water droplets or ice crystals that are
much larger than  and they hence scatter light of all
wavelengths nearly equally. Hence clouds appear
white.
(iii) At sunrise or sunset the sun appears reddish :
The scattering of light also explains the raddish
appearance of sun at sunrise or sunset. At sunrise or
sunset, the sun is near the horizon and the sunrays
reach the earth after passing through a maximum
distance in the atmosphere . During this passage, the
light is scattered by air molecules and fine dust
particles. Since scattering  1/4, most of the blue and
neighbouring-coloured light is scattered out before
reaching the observer. Hence the light received by the
observer is predominantly red. (For a similar reason,
the sun appears orange-red in fog or mist.)
At noon, when the sun is overhead, the sunrays travel
minimum distance in the atmosphere and there is little
scattering. Hence the sun appears almost while (infact,
slightly yellowish because some blue light is
scattered).
TOTAL INTERNAL REFLECTION
The phenomenon of reflection when a ray of light
travelling from a denser to rarer medium is sent back
to the same denser medium, provided when it strikes
the interface of the denser and the rarer media at an
angle greater than the critical angle, is called total
internal reflection.
When a ray of light falls on the interface separating
denser and rarer medium, it is refracted as shown in
NTSE STAGE-I_PAGE # 16
figure. As the angle of incidence increases, the refracted
ray bends towards the interface. At a particular angle of
incidence, the, refracted light travels along the interface
and the angle of refraction becomes 90º. The angle of
incidence for which angle of refraction becomes 900 is
called critical angle iC.
coated with a thin layer of material of refractive index
less than the refractive index of the strand.
(If refractive index of the core is say 1.7 then refractive
index of the coating is 1.5). The coating or
surrounding of optical strands is known as cladding.
The sleeve containing a bundle of optical fibres is called
a light pipe.
When light falls at one end of the optical fibre, it gets
total internally refracted into the fibre. The refracted ray
of light falls on the interface separating fibre and coating
at an angle which is greater than the critical angle. The
total internal reflection takes place again and again as
shown in figure below. The light travels the entire length
of the fibre and arrives at the other end of the fibre
without any loss in its intensity even if the fibre is
rounded or curved.
Figure : Ray diagram showing total internal reflection
When the angle of incidence becomes greater than
the critical angle, there is no refracted light and all the
light is reflected in the denser medium. This
phenomenon is known as total internal reflection.
Figure : Structure of optical fibre
(a) Conditions for total Internal Reflection :
(ii) Sparking or brilliance of a diamond
(i) The light should travel from denser to rarer medium.
(ii) The angle of incidence must be greater than the
critical angle for the given pair of media.

IMPORTANT NOTE :
During total internal reflection of light, the whole incident
light energy is reflected back to the parent optically
denser medium.
(i) Critical angle of a medium depends upon the
wavelength of light.
Critical angle  wavelength :
Greater the wavelength, greater will be the critical
angle. Thus, critical angle of a medium will be
maximum for red colour and minimum for violet colour.
The refractive index of diamond is 2.5 which gives, the
critical angle as 24º. The faces of the diamond are cut
in such a way that whenever light falls on any of the
faces, the angle of incidence is greater than the critical
angle i.e. 24º. So when light falls on the diamond, it
suffers repeated total internal reflections. The light
which finally emerges out from few places in certain
directions makes the diamond sparkling.
(iii) Shining of air bubble in water
The critical angle for water-air interface is 48º 45. When
light propagating from water (denser medium) is
incident on the surface of air bubble (rarer medium) at
an angle greater than 480 45’, the total internal reflection
takes place. Hence the air bubble in water shines
brilliantly.
(ii) Critical angle depends upon the nature of the pair
of media. Greater the refractive index, lesser will be
the critical angle.
(iii) Image formed due to total internal reflection is much
brighter because total light is reflected back into the
same medium and there is no loss in intensity of light.
(b) Some Phenomena due to total Internal
Reflection :
Figure : Shining of air bubble in water
(i) Optic pipe and optical fibres
(iv) Mirage :
Optical fibre is extremely thin (radius of few microns)
and long strand of very fine quality glass or quartz
Mirage is an optical illusion of water observed generally in
deserts when the inverted image of an object
(e.g. a tree) is observed along with the object itself on a hot
day.
NTSE STAGE-I_PAGE # 17
(a) Primary Colours of Light :
Red, green and blue are primary colours of light and
they produce white light when added in equal
proportions. All colours can be obtained by mixing these
three colours in different proportions.
Figure : A mirage formation in deserts
Due to the heating of the surface of earth on a hot day,
the density and hence the refractive index of the layers
of air close to the surface of earth becomes less. The
temperature of the atmosphere decreases with height
from the surface of earth, so the value of density and
hence the refractive index of the layers of air at higher
altitude is more. The rays of light from distant objects
(say a tree) reaches the surface of earth with an angle
of incidence greater than the critical angle. Hence the
incident light suffers total internal reflections as shown
in the figure. When an observer sees the object as
well as the image he gets the impression of water
pool near the object.
(b) Secondary Colours or Composite Colours
of Light :
The colours of light produced by adding any of primary
colours are called secondary colours. Cyan, magenta
and yellow are secondary colours of light.
Red + Green = Yellow
Green + Blue = Cyan
Red + Blue = Magenta
The method of producing different colours of light by
adding the primary colours is called colour addition.
(A) The mirage formed in hot regions is called inferior
mirage.
(B) Superior mirage is formed in cold regions. This
type of mirage is called looming.
(v)
Uses of Optical Pipe :
(c) Complementary Colours of Light :
(ii) Optical fibres are used in the manufacture of medical
instruments called endoscopies. Light pipe is inserted
into the stomach of the human being. Light is sent
through few optical fibres of the light pipe. The reflected
light from the stomach is taken back through the
remaining optical fibres of the same light pipe. This
helps the doctors to see deeply into the human body.
Hence the doctor can visually examine the stomach
and intestines etc. of a patient.
(iii) They are used in telecommunication for transmitting
signals. A single fibre is able to transmit multiple
signals (say3000) simultaneously without interference,
whereas the electric wire can preferably transmit one
signal at a time.
The lights of two colours which when added in equal
proportions produce white light are called
complementary colours of light and the two colours
are called complements of each other.
For example, yellow and blue light are complementary
colours of light because when they mixed in equal
proportions, they produce white light. We can also find
the pairs of complimentary colours of light as follows.
Complimentary
colours
(Red + Green ) + Blue = Yellow + Blue = White
Red + (Green + Blue) = Red + Cyan = White
(Red + Blue ) + Green = Magenta + Green = White
R
(iv) Optical fibres are used to transmit the images of
the objects.
(v) Optical fibres are used to transmit electrical signals
from one place to another. The electrical signals are
converted into light by special devices called
transducers, then these light signals are transmitted
through optical fibres to distant places.
White
G
nta
ge
Ma
Ye
llow
(i) Optical fibres are used to transmit light without any
loss in its intensity over distances of several
kilometer.
Cyan
Colour triangle
B
NTSE STAGE-I_PAGE # 18
The above results can be diagrammatically represented
in the form of a triangle as shown in figure below. The
outer limbs of the figure show the results of the addition
of primary colours red, green and blue. The
complementary colour pairs such as red and cyan are
opposite to each other.
(d) Primary Colours of Pigment :
Pigments are those substances that give colour to an
object. The colour of a pigment as seen by us depends
on what components of light it absorb or subtract from
white light before reflecting the rest to our eyes. A
primary colour (cyan, magenta, yellow) of a pigment is
due to a primary colour of light being subtracted from
white light.
White – Red = Blue + Green = Cyan
White – Green = Red + Blue = Magenta
White – Blue = Red + Green = Yellow
Mixing CMY (cyan, magenta, yellow) pigment in the
correct proportions can produce millions of colour. If
equal amount of pure CMY pigments are mixed, we
should get a black pigment. However, printers use
black ink in addition to CMY inks to get good results.
Yellow
White
Cyan
Subtractive Primaries
NTSE STAGE-I_PAGE # 19
ELECTRICITY
ELECTRIC CHARGE
(a) Definition :
Electric charge may be defined as the intrinsic property
of certain fundamental particles (electron, proton, etc.)
due to which they produce electric and magnetic
effects.
(b) Types of Electric Charge :
There are two types of charges. They are :
(i) Positive charge - A body having deficiency of
electrons.
(ii) Negative charge- A body having excess of
electrons.
(c) Charging of a body :
There are a number of methods to charge a body as:
(i) Charging by friction
(ii) Charging by conduction
(iii) Charging by induction etc.
(a)
(b)
(iii) Charging by induction : The process of charging
a body by keeping it near a charged body, but not
touching it, is called charging by induction.
Take a metal rod A on an insulating stand. Bring a
positively charged conductor B with an insulating
handle near it. Keeping the charged conductor with
your finger. Now, remove your finger first and then the
charged conductor. The uncharged conductor
becomes negatively charged figure.
(i) charging by friction :
Whenever two bodies (at least one non conductor) are
rubbed against each other, heat is produced due to
friction present between them. Due to this heat
produced, electrons in both the bodies are excited.
The body having more electron affinity attracts some of
the electrons from other body. Both the bodies develop
equal and opposite charges by this method.
POSITIVE CHARGE
NEGATIVE CHARGE
1. Glass Rod
1. Silk cloth
2. Fur or woolen cloth
2. Ebonite, Amber,
Rubber rod
3. Woolen coat
3. Plastic seat
4. Woolen carpet
4. Rubber shoes
5. Nylon or Acetate
5. Cloth
6. Dry hair
6. Comb
(d) Properties of Electric Charge :
(i) Like charges repel and unlike charges attract each
other.
////////////////////////////
Attraction
+
Repulsion
+
+ –
(ii) Charge is a scalar quantity
Note : The object in above table must be in given pair.
(ii) Charging by conduction :
If an uncharged conductor is touched with a
positively or negatively charged conductor, then the
uncharged conductors also acquires the charged
possessed by the charged conductor .This process
is called charging by conduction.
Take an uncharged metal rod A and place it on an
insulating stand as shown in figure (a) bring a positively
charged conductor B with an insulating handle near it
and touch the metal rod A figure(b). You will observe
that the uncharged metal rod becomes positively
charged. Try the same activity with a negatively charged
conductor. Observe the charge on the uncharged
conductor.
(iii) Charge is always quantized : The amount of charge
on a charged body is always in integral multiple of the
elementary charge the fractional multiple is not
possible.
(iv) Charge is conserved: Whenever two bodies are
charged by rubbing, one gets positively charged and
the other negatively charged. The net charge on the
two bodies, however, remains zero–the same as that
before rubbing. In other words, charge is conserved.
It can neither be created nor destroyed. The only thing
that happens on rubbing is that charged particles
(electrons) get transferred from one body to the other.
NTSE STAGE-I_PAGE # 20
In some phenomena, charged particles are created.
But even then the conservation of charge holds. For
example, a free neutron converts itself into an electron
and the proton taken together is also zero. So, there is
no change in the conversion of a neutron to an electron
and a proton.
(v) Charge is always associated with mass.
(vi) Total charge of system remains conserved .
ILLUSTRATIONS
1.
Sol.
A charge Q is placed at each of the opposite
corners of a square. A charge q is placed at
each of the other two corners. If the net
electrical force on Q is zero, then Q/q equals
Since Fnet is zero
kqQ
(e) Unit of Charge :
The S.I. unit of charge is coulomb abbreviated as C.
One coulomb of charge is equal to the charge on
625 × 1016 electrons.
1 coulomb = charge on 625 × 1016 electrons
or 6.25× 1018 electrons
Thus, when we say that a body has a positive charge
of one coulomb (i.e. + 1C) it means that the body has a
deficit of 625 × 1016 electrons from the normal due to
a2
[ 2] 
kQ 2
2a2
0
share.
Q
 –2 2
q
STATIC AND CURRENT ELECTRICITY
(a) Static electricity :
A branch of physics which deals with the study of the
electric charges at rest and their effects is known as
electrostatic or static electricity.
(b) Current electricity
A branch of physics which deals with the study of the
electric charges in motion and their effects is known
as current electricity.
COULOMB’S LAW
Charles Augustine de Coulomb studied the interaction
forces of charged particles in detail in 1784. He used a
torsion balance. On the basis of his experiments he
established Coulomb’s law. According to this law the
magnitude of the electric force between two point
charges is directly proportional to the
product of the magnitude of the two charges and
inversely proportional to the square of the
distance between them and acts along the straight
line joining the two charges.
In mathematical terms, the force that each of the two
point charges q1 and q2 at a distance r apart exerts on
the other can be expressed as–
F= k
q1q2
r2
This force is repulsive for like charges and attractive
for unlike charges.
Where k is a constant of proportionality. k =
1
4  0 ,
here 0 is absolute permittivity of free space.
The force is directed along the line joining the centres
of the two charged particles.
ELECTRIC FIELD AND ELECTRIC POTENTIAL
(a) Electric Field :
Electric field due to a given charge is defined as the
space around the charge in which electrostatic force
of attraction or repulsion due to charge can be
experienced by any other charge. If a test charge
experiences no force at a point, the electric field at that
point must be zero.
Electric field intensity at any point is the strength of
electric field at that point. It is defined as the force
experienced by unit positive charge placed at that point.
If F is the force acting on a test charge +q0 at any point
then electric field intensity at this point is given by
E
F
q
0
Electric field is a vector quantity and its S.I. unit is
Newton per coulomb (N/C).
(b) Electric Potential :
The electric potential at a point in an electric field is
defined as the amount of work done in moving a unit
+ve charge from infinity to that point, without acceleration
or without a change in K.E., against the electric force
due to the electric field.
Mathematically,
V W
q
Since work is measured in joule and charge in
coulomb, therefore electric potential is measured in
joule per coulomb (J/C). This unit occurs so often in
NTSE STAGE-I_PAGE # 21
our study of electricity, so it has been named as volt, in
honour of the scientist Alessandra Volta (the inventor
of the voltaic cell).
1 joule
The voltmeter is connected in parallel across the points
where the potential difference is to be measured. A
voltmeter has a high resistance so that it takes a negligible
current from the circuit.
1 Volt = 1 coulomb
Potential is a scalar quantity, therefore it is added
algebraically. For a positively charged body potential is
positive and for a negatively charged body potential is
negative.

We can say potential is the electrical state of a
conductor which determines the direction of flow
charge when the two conductor are kept in contact.
(c) Electric Potential Difference :
Consider a charge Q placed at a point P. Let A and B be
two other points (B being closer to A) as shown in
figure.
Q
B
This rate of flow electric charge from one body to another
through a conductor such as metal wire is called
electric current and its direction is opposite to direction
of flow of electrons.
Thus, if Q is the charge which flows through a
conductor in time t, then the electric current is given
by
Current (I) =
From infinity
P
The quantity VB – VA is called the potential difference
between points A and B in the electric field of charge Q.
Mathematically we have,
WB WA

q
q
I=
or
Q = It
Note : The electric current is a scalar quantity.
(a) Unit of current :
Consider a charge Q placed at a point P as shown in
figure. If another charge q of the same sign is now
brought from a very far away distance (infinity) to point
O near P, then charge q will experience a force of
repulsion due to charge Q. If charge q is still pushed
towards P, work is done. This work done is the potential
energy of the system of these two charges.
P
q
O
1 ampere =
1 coulomb
1 sec ond
or 1 A = 1 C s-1
(b) Direction of Electric Current :
ELECTRIC POTENTIAL ENERGY
r
Q
t
or
Electric potential difference is also measured in volt.
Q
Ch arg e (Q)
Time ( t )
q
A
VB – VA 
ELECTRIC CURRENT
q
From infinity
Thus, the electric potential energy of a system of
charges is defined as the amount of work done in
bringing the various charges from infinite separation
to their present positions to form the required
system. It is denoted by U. For the system of two
charges separated by distance r as shown in figure,
the electric potential energy is given by :
kQq
U=
r
Electric potential energy is the from of energy, therefore
it is measured in joule (J). The potential difference is
measured by means of an instrument called voltmeter.
When electricity was invented a long time back, it was
known that there are two types of charges : positive
charges and negative charges, but the electron had
not been discovered at that time. So, electric current
was considered to be a flow of positive charges and
the direction of flow of the positive charges was taken
to be the direction of electric current. Thus, the conventional
direction of electric current is from positive terminal of
a cell (or battery) to the negative terminal through the
circuit.
W hen two charged bodies at different electric
potentials are connected by a metal wire, an electric
current will flow from the body at higher potential to the
one at lower potential till they both acquire the same
potential. Let two oppositely charged metal conductors
A and B are held on insulated stands.
Electric Current
+
Positively
Charged
Conductor
–
A
wire
B
Negatively
Charged
Conductor
Insulated Stand
The positively charged conductor A is said to be at
higher potential and the negatively charged conductor
NTSE STAGE-I_PAGE # 22
B is said to be at a lower potential. Thus, there is a
potential difference between the oppositely charged
conductors A and B. So, when we join the positively charged
conductor A to negatively charged conductor B by a metal
wire, then electric current starts flowing from A to B.
Potential
difference (V)
(c) How the Current Flows in a Wire :
As electric current is the flow of electrons in a metal
wire (or conductor) when a cell or battery is connected
across its ends. A metal wire has plenty of free electrons
in it. When the metal wire has not been connected to a
source of electricity like a cell or a battery, then the
electrons present in it move at random in all the
directions between the atoms of the metal wire as
shown in figure below.
e–
e–
e
–
e–
4V
3V
2V
V
x
x
x
x
Current (A)
Slope of graph, tan =
V
=R
I
ELECTRICAL RESISTANCE
(a) Definition :
e–
e
–
Metal Wire
e–
–
e
The property of a conductor due to which it opposes
the flow of current through it, is called resistance. The
resistance of a conductor is numerically equal to the
ratio of potential difference across its ends to the
current flowing through it.
When a source of electricity like a cell or a battery is
connected between the ends of the metal wire, then
an electric force acts on the electrons present in the
wire. Since the electrons are negatively charged, they
start moving from negative end to the positive end of
the wire and this flow of electrons constitutes the
electric current in the wire.

Resistance =
or
R=
Potential difference
Current
V
I
( b ) Unit of Resistance :
–
–
–
–
e
e
e
e –
e–
e–
e–
e–
Direction of conventional Current
+
+ –
Cell
OHM'S LAW
`
The S.I. unit of resistance is ohm, which is denoted by
the symbol  .
When a potential difference of 1 volt is applied to the
ends of the conductor and a current of 1 ampere flows
through it, then resistance of the conductor will be 1
ohm.
(c) Factors affecting the Resistance of a
Conductor :
Resistance depends upon the following factors:-
It states that the current passing through a conductor
is directly proportional to the potential difference across
its ends, provided the temperature and other physical
conditions (mechanical strain etc.), remain unchanged
i.e.,   V or V  
or V = R
W here R is a constant called resistance of the
conductor.
The relation R = V/ is referred to as Ohm’s law, after
the German physicist George Simon Ohm (1789 - 1854),
who discovered it.
It is quite clear from the above equation that
(i) The current  is proportional to the potential difference
V between the ends of the resistor.
(ii) If V is constant, then current  is inversely
proportional to the resistance.
Now, plot a graph between the current and the potential
difference. we will get a straight line graph.
(i) Length of the conductor.
(ii) Area of cross-section of the conductor (or thickness
of the conductor).
(iii) Nature of the material of the conductor.
(iv) Temperature of the conductor.
Mathematically : It has been found by experiments
that :
(i) The resistance of a given conductor is directly
proportional to its length i.e.
R L
..........(i)
(ii) The resistance of a given conductor is inversely
proportional to its area of cross-section i.e.
R
1
A
..........(ii)
from (i) and (ii)
NTSE STAGE-I_PAGE # 23
R
L
A
 R =
ñ L
A
..........(iii)
Where  (rho) is a constant known as resistivity of the

material of the conductor. Resistivity is also known as
specific resistance.
Effect of stretching of a wire on resistance:
In stretching, the density of wire usually does not
change. Therefore
Volume before stretching = Volume after stretching

R’ = 
I 

 r  
A

R’ =
.4I
= 4R
r 2
(d) Resistivity :
 1A 1   2 A 2
Resistivity,
R 2  2 A1


and
R1  1 A 2
If information of lengths before and after stretching
is given, then use
2I
I'
= 
r '2
A'
A1  2

A 2 1
ñ =
RA
L
..........(iv)
By using this formula, we will now obtain the definition
of resistivity. Let us take a conductor having a unit area
of cross-section of 1 m2 and a unit length of 1 m. So,
putting A = 1 and L = 1 in equation (iv), we get:
Resistivity,  = R
(i) Definition of resistivity :
R2   2 
 
R1   1 
2
If information of radius r1 and r2 is given then use
2
A
 1
1 A 2
‘’ =
R 2  A1 


R1  A 2 
2
r 
  1 
 r2 
The S.I. unit of resistivity is ohm-metre which is written
in symbols as -m.
If R0 is the resistance of the conductor at 0ºC and Rt is
the resistance of the conductor at tºC then the relation
between R0 and Rt is given by,
Rt = Ro( 1  áÄt )

[Here t = t – 0 = t]
R t – R0
R0 t
Here,  =Temperature Coefficient of Resistance,
t = temperature in oC
2.
The length of a given cylindrical wire is increased by
100%. Due to the consequent decrease in diameter
the change in the resistance of the wire.
Sol. Given, I, = I + 100% I = 2I
Initial volume = final volume
ie, r2 I = r’2 I’
or
r’2 =
I
r 2I
= r2 ×
2I
I'
or
r’2 =
r2
2
ohm  (metre )2
= ohm - metre
metre
4
Dependency of resistance on temperature :
or
The resistivity of a substance is numerically equal to
the resistance of a rod of that substance which is
1 metre long and 1 metre square in cross-section.
Unit of resistivity,
Resistivity of a substance does not depend on its
length or thickness. It depends only on the nature of
the substance. The resistivity of a substance is its
characteristic property. So, we can use the resistivity to
compare the resistances of two or more substances.
(ii) Importance of resistivity :
A good conductor of electricity should have a low
resistivity and a poor conductor of electricity should
have a high resistivity. The resistivity of alloy are much
more higher than those of the pure metals.
It is due to their high resistivities that manganin and
constantan alloys are used to make resistance wires
used in electronic appliances to reduce the current in
an electrical circuit.
Nichrome alloy is used for making the heating
elements of electrical appliances like electric irons,
room-heaters, water-heaters and toasters etc.
because it has very high resistivity and it does not
undergo oxidation (or burn) even when red-hot.
(iii) Factor affecting the resistivity :
It depends on : Nature of conductor :
The resistivity is less for a good conductor and is large
for a bad conductor.
NTSE STAGE-I_PAGE # 24
(ii) Parallel combination of resistors :
Consider two resistors R1 and R2 connected in parallel
as shown in figure. When the current  reaches point
‘a’, it splits into two parts 1 going through R1 and 2
going through R2. If R1 is greater than R2, then 1 will be
less than 2 i.e. the current will tend to take the path of
least resistance.
Temperature :
The resistivity of conductors (like metals) is very low. The
resistivity of most of the metals increases with
temperature. On the other hand the resistivity of semiconductors like silicon and germanium is in between
those of conductors and insulators and decreases on
increasing the temperature. Semi-conductors are proving
to be of great practical importance because of their
marked change in conducting properties with
temperature and impurity concentration.
(e) Conductivity :
The reciprocal of resistivity is called conductivity that
means
meter

1
 and its S.I. unit is  –1m–1 or siemen

Thus in parallel combination the equivalent resistance
1
–1.
RP
Combination of Resistances Resistors)
We can combine the resistances lengthwise (called
series) or we can put the resistances parallel to one
another. Thus, the resistances can be combined in
two ways :
(i) series combination (ii) parallel combination
=
1
R1
+
1
R2
An extension of this analysis to three or more resistors
in parallel gives the following general expression
1
RP

(i) Series combination of resistors :

1
R1

1
R2

1
 .......... ..
R3
Features of parallel combination :
(A) The sum of the reciprocals of the individual
resistance is equal to the reciprocal of equivalent
resistance(RP).
Consider three resistors of resistances R1, R2 and R3
connected in series to cell of potential difference V as
shown in figure. Since the three resistors are
connected in series therefore the current  through each
of them is same.
(B) The currents in various resistors are inversely
proportional to the resistances, higher the resistance
of a branch, the lower will be the current through it. The
total current is the sum of the currents flowing in the
different branches.
(C) The voltage across each resistor of a parallel
combination is the same and is also equal to the
voltage across the whole group considered as a unit.
Rs
Thus in series combination the equivalent resistance
is the sum of the individual resistances. For more
resistors, the above expression would have beenRs = R1 + R2 + R3 +..................


3.
Features of series combination :
Equivalent resistance between points A and B in
the given diagram is :
In a circuit, if the resistors are connected in series :
(A) The current is same in each resistor of the circuit.
NOTE : For n equal resistances R = n2
p
Sol:
Suppose
(B) The resistance of the combination of resistors is
equal to sum of the individual resistors.
(C) The total voltage across the combination is equal
to the sum of the voltage drop across the individual
resistors.
Rearrange
(D) The equivalent resistance is greater than that of
any individual resistance in the series combination.
Parallel combination
NTSE STAGE-I_PAGE # 25
R AC

1 1 1
 
R R R
,
1
1 1 1
  
R CB R R R
Series combination

RAB = RAC + RCB
=
suitable values of the resistances. Thus, in null
deflection state, we have :
Wheatstone bridge is an arrangement of four resistors
in the shape of a quadrilateral which can be used to
measure unknown resistance in terms of the
remaining three resistances.
The arrangement of Wheatstone bridge is shown in
figure below. Out of four resistors, two resistances R1,
R2 and R3, R4 are connected in series and are joined in
parallel across two points a and c. A battery of e.m.f. E
is connected across junctions a and c and a
galvanometer (G) between junction b and d. The keys
K1 and K2 are used for the flow of current in the various
branches of bridge.
Principle of Wheatstone Bridge :
When key K1 is closed, current i from the battery is
divided at junction a in two parts. A part i1 goes through
R1 and the rest i2 goes through R3. When key K2 is
closed, galvanometer shows a deflection.
...(i)
Similarly :
Vb – Vc = Vd – Vc
or
i1 R2 = i2 R4
On dividing equation (i) by (ii), we get
R R
2R

=
.
3 3
3
WHEATSTONE BRIDGE
Va – Vb = Va – Vd
i1 R1 = i2 R3
or
i2 R 3
i1 R1
=
i1 R 2
i2 R 4
or
...(ii)
R1 R 3

R 2 R 4 ...(iii)
Equation (iii) states the condition of balanced bridge.
Thus, in null deflection condition the ratio of
resistances of adjacent arms of the bridge are same.
The resistor of unknown resistance is usually
connected in one of the arm of the bridge. The
resistance of one of the remaining three arms is
adjusted such that the galvanometer shows zero
deflection. If resistance of unknown resistor is R4. Then
 R2 

 R1 
R4 = (R3) 
For better accuracy of the bridge one should choose
resistances R1, R2, R3 and R4 of same order.
6. Find the current flowing through the 36 V battery in
the given circuit.
2
4
1
Sol.
6
5
2
36
v
6
Redraw the ckt
Using wheat stone bridge concept
The direction of deflection depends on the value of
potential difference between b and d. When the value
of potential at b and d is same, then no current will flow
through galvanometer. This condition is known as the
condition of balanced bridge or null deflection
condition. This situation can be obtained by choosing
I=
36 V
= 4A.
( 4  5)
NTSE STAGE-I_PAGE # 26
SUPER CONDUCTOR AND ITS APPLICATIONS
Prof. K. Onnes in 1911 discovered that certain metals
and alloys at very low temperature lose their
resistance considerably. This phenomenon is known
as super-conductivity. As the temperature decreases,
the resistance of the material also decreases, but when
the temperature reaches a certain critical value (called
critical temperature or transition temperature), the
resistance of the material completely disappears i.e. it
becomes zero. Then the material behaves as if it is a
super-conductor and there will be flow of electrons
without any resistance whatsoever. The critical
temperature is different for different material. It has
been found that mercury at critical temperature 4.2 K,
lead at 7.25 K and niobium at critical temperature 9.2
K become super-conductor.
Applications of super conductors :
(i) Super conductors are used for making very strong
electromagnets.
(ii) Super conductivity is playing an important role in
material science research and high energy particle
physics.
(iii) Super conductivity is used to produce very high
speed computers.
(iv) Super conductors are used for the transmission of
electric power.
HEATING EFFECT OF CURRENT
When the ends of a conductor are connected to a
battery, then free electrons move with drift velocity and
electric current flows through the wire. These electrons
collide continuously with the positive ions of the wire
and thus the energy taken from the battery is dissipated.
To maintain the electric current in the wire, energy is
taken continuously from the battery. This energy is
transferred to the ions of the wire by the electrons. This
increases the thermal motion of the ions, as a result
the temperature of the wire rises. The effect of electric
current due to which heat is produced in a wire when
current is passed through it is called heating effect of
current or Joule heating. In 1841 Joule found that when
current is passed through a conductor the heat
produced across it is :
(i) Directly proportional to the square of the current
through the conductor i.e. H  I2
(ii) Directly proportional to the resistance of the
conductor i.e. H  R
(iii) Directly proportional to the time for which the current
is passed i.e. H  t
Combining the above three equations we have
H  I2Rt
or
H=
I2 Rt
(in calorie)
J
Where J is called Joule’s mechanical equivalent of
heat and has a value of J = 4.18 J cal–1. The above
equation is called Joule’s law of heating.
In some cases, heating is desirable, while in many
cases, such as electric motors, generators or
transformers, it is highly undesirable. Some of the
devices in which heating effect of an electric current is
desirable, are incandescent lamps, toasters, electric
irons and stoves. The tungsten filament of an
incandescent lamp operates at a temperature of 27000C.
Here, we see electrical energy being converted into
both heat and light energy.
(a) Electric Energy :
The fact that conductors offer resistance to the flow of
current, means that work must be continuously done
to maintain the current. The role of resistance in
electrical circuits is analogous to that of friction in
mechanics. The amount of work done by current ,
flowing through a wire of resistance R during the time
t is calculated by W = QV
but as
Q=×t
Therefore, the amount of work done, W is
W=V××t
By substituting the expression for V from Ohm’s law,
V = R
we finally get
W = 2 Rt
This shows that the electrical energy dissipated or
consumed depends on the product of the square of
the current I, flowing through the resistance R and the
time t.
(i) Commercial unit of electrical energy (Kilowatt hour) :
The S.I. unit of electrical energy is joule and we know
that for commercial purposes we use a bigger unit of
electrical energy which is called “kilowatt - hour”. One
kilowatt - hour is the amount of electrical energy
consumed when an electrical appliance having a power
rating of 1 kilowatt and is used for 1 hour.
(ii) Relation between kilowatt hour and Joule :
Kilowatt-hour is the energy supplied by a rate of
working of 1000 watts for 1 hour.
1 kilowatt-hour = 3600000 joules
1 kWh = 3.6 × 106 J
(b) Electric Power :
The rate at which electric energy is dissipated or
consumed, is termed as electric power. The power P
is given by,
P = W/t = I2 R
The unit of electric power is watt, which is the power
consumed when 1A of current flows at a potential
NTSE STAGE-I_PAGE # 27
when it consumes 12 W power What should be the
resistance of the resister so that the lamp work as
designed ?
difference of 1 V.
(i) Unit of power :
The S.I. unit of electric power is ‘watt’ which is denoted
by the letter W. The power of 1 watt is a rate of working
of 1 joule per second.
12V
A bigger unit of electric power is kilowatt.
Lamp
1 kilowatt (kW) = 1000 watt.
Power of an agent is also expressed in horse power (hp).
Sol:
1 hp = 746 watt
(ii) Formula for calculating electric power :
R=
We know,
Work
Power, P =
Time
and
Work, W = V × I × t joule

P=
VIt
t
P = V × I
at zero (the centre of the scale) for zero current flowing
through it. It can deflect either to the left or to the right of
V
=R
I
the zero mark depending on the direction of current.
Galvanometers are of two types :
V=I×R
P=I×R×I
P = I2 × R
(i) Moving coil galvanometer
(ii) Moving magnet galvanometer
Power P in terms of V and R :
We know,
P=V×I
From Ohm’s law
V
I=
R
V
P=V×
R
V2
P =
R
It is used to make ammeter and voltmeter as follows:
(a) Ammeter :
(ii) Calculation of Electric bill :
Energy consumued by electric appliances is given by
the formula.
Electricity energy (in kWh) =
Power (in watt )  No. of appliances  time(in hrs.)
(in kWh or unit)
1000
Rating
of
Electrical
Every electrical appliance like an electric bulb, radio or
fan has a label or engraved plate on it which tells us
the voltage (to be applied) and the electrical power
consumed by it. For example, if we look at a particular
bulb in our home, it may have the figures 220 V, 100 W
written on it. Now, 220 V means that this bulb is to be
used on a voltage of 220 volts and 100 W which means,
it has a power consumption of 100 watts or 100 joules
per second, when supplied a voltage of 220 volt.
4.
A galvanometer is an instrument that can detect the
presence of a current in a circuit. The pointer remains
Now from Ohm’s law we have,
(c) Power-Voltage
Appliances :
VB – VA
12 – 4
=
= 8/3 .

3
GALVANOMETER
Power P in terms of I and R :

Power = 12 w , voltage = 4v
P = VI  12 = 4I  I = 3A.
A lamp is connected in series with a resister to a 12 V
battery as in the circuit shown. The lamp is designed
to work when the voltage drop across it is 4 V and
Ammeter is an electrical instrument which measures
the strength of current in ‘ampere’ in a circuit. is always
connected in series in circuit so that total current (to be
measured) may pass through it. For an ammeter of
good quality, the resistance of its coil should be very
low so that it may measure the strength of current
accurately (without affecting the current passing
through the circuit). The resistance of an ideal ammeter
is zero (practically it should be minimum).
In electric circuit, the positive terminal of an ammeter
is connected to positive plate and negative terminal is
connected to negative plate of battery.
(b) Voltmeter :
It is an electrical instrument which measures the
potential difference in ‘volt’ between two points of
electric circuit. It’s construction is similar as that of
ammeter. The only difference between ammeter and
voltmeter is that ammeter has its negligible
(approximately zero) resistance so that it may measure
current of circuit passing through it more accurately
giving the deflection accordingly, while the voltmeter
passes negligible current through itself so that potential
difference developed due to maximum current passing
through circuit may be measured.
Ideal voltmeter has infinite resistance of its own. When
NTSE STAGE-I_PAGE # 28
ideal voltmeter is connected parallel to a part of an
electric circuit, it passes zero amount of current through
itself from the circuit so that measurement of potential
difference across the points of connection may be
perfectly accurate.
ELECTRICAL SAFETY
(a) Local Earthing :
In a house , the local earthing is made near the kWh
meter. For this purpose, a 2-3 metre deep hole is dug
in the ground. A copper rod (or a thick copper wire)
placed inside a hollow insulating pipe, is put in the
hole. A thick copper plate of dimensions 50 cm × 50
cm is welded to the lower end of the copper rod and it
is buried in the ground. The plate is surrounded by a
mixture of charcoal and salt to make a good earth
connection To deep the ground damp, water is poured
through the pipe from time to time. This forms a
conducting layer between the plate and the ground.
The upper end of the copper rod is joined to the earth
connection at the kWh meter.
Safety by the local earthing : If due to some reason
such as short circuiting, an excessive current flows
through the line wires, it will pass to earth through the
earth wire if there is local earthing, otherwise it may
cause a fire due to overheating of the line wires.
(b) Earthing of an appliance :
For earthing of an electrical appliance (such as
refrigerator, toaster, geyser, electric iron, electric,
cooler,etc.) which we handle physically, the earth wire
(green or yellow) of the cable is connected to the outer
metallic case of the appliance. Figure shows the
symbol for earthing an appliance.
It may be mentioned here that most often the metal
body part of the appliance is painted.
The paint provides an insulating layer on the metal
body of the appliance. To make earth connection
therefore, the paint must be removed from the body
part where connection is to be made.
Safety by earthing of an appliance :
When the live wire of a faulty appliance comes in direct
contact with its metallic case due to break of insulation
after constant use (or otherwise), the appliance
acquires the high potential of the live wire. A person
touching it will get a fatal shock because current flows
through his body to the earth . But if the metallic case of
the appliance is earthed, then as soon the live wire
comes in contact with the metallic case of the
appliance, immediately a heavy current flows through
the case of appliance to the earth (since the metallic
case has almost zero resistance) and the fuse
connected in the circuit of the appliance or in line blows
off, so the appliance gets disconnected. Thus, the
person touching the defective appliance does not get
a shock and the appliance is also saved from being
damaged. It should be noted that for this, it is essential
that the fuse must be connected in the live wire only. If
the fuse is in the neutral wire, then although the fuse
burns due to the flow of heavy current, but the appliance
remains at the supply voltage os that on touching the
appliance, current flows through the appliance to the
person, with the result that the person touching the
appliance may get a fatal shock.
(c) Fuse :
An electric fuse is an easily fusible wire of short length
put into an electrical circuit for protection
purposes. It is arranged to melt (“blow”) at a definite
current. It is an alloy of lead and tin (37% lead + 63% tin).
It has a low resistivity and low melting point. As soon
as the safe limit of current exceeds, the fuse “blows”
and the electric circuit is cut off.
(d) Miniature Circuit Breaker :
These days a device called a miniature circuit breaker
(MCB) is also used instead of or in addition of fuses, in
the household electric circuits. It is a switch that
automatically switches off a circuit if the current in it
exceeds the specified maximum limit.
NTSE STAGE-I_PAGE # 29
COLOUR CODING OF WIRES
An electric appliance is provided with a three-core
flexible cable. The insulation on the three wires is of
different colours. The old convertion is red for live, black
for neutral and green for earth. The new international
convention is brown for live, light blue for neutral and
green (or yellow) for earth.
ALTERNATING CURRENT (AC)
A current which is change with respect to time is
called Alternating Current
Difference between DC and AC
Direct Current (D.C.)
(1) A current which does not
(i) a fire
(ii) an electric shock.
(i) A fire is caused due to over heating of line wires (or
cable for various reasons such as break of insulation
or short circuiting etc. To avoid it, one must use wires
(or cable) of current carrying capacity higher than the
current which can flow through the circuit when using
all the appliances at the same time.
(ii) An electric shock may be caused either due to poor
insulation of wires of when the electric appliances are
touched with wet hands. To avoid it, the insulation of
wires must he of good quality and it should be checked
from time to time particularly when they become old,
so that no wire is left naked. Apart from this, an electrical
appliance such as switch, plug, socket, electric wire,
etc., should never be operated (or touched ) with wet
hands and they should always be kept in a dry
condition.
(1) A current which changes
change with respect to time
is called Direct Current.
SAFETY PRECAUTIONS WHILE USING ELECTRICITY
There are two major dangers while using electricity.
They are :
Alternating Current (A.C.)
(2) It is produced by cell
with respect to time is called
Alternating Current.
(2) It is produced by thermal, water,
and battery.
wind, nuclear power plant.
(3) It is less harmful.
(3) It is harmful.
(4)
(4)
0
t
(5) It is measured by
ammeter.
(6) It is base of electronics.
0
t
(5) It is measured by hot wire
instruments.
(6) It is base of electricity.
ADVANTAGES OF AC OVER DC
More than 90% of electric power generated in the world
is in the form of alternating current and power generated
in the form of DC is less than 10%. In India AC changes
its direction after every 1/100 of second i.e. the
frequency of AC is 50 Hz. The advantages of AC over
DC are as follows :
(i) AC can be transmitted to distant places with very
small loss in AC power.
HIGH TENSION WIRES
Each wire in a cable is capable of withstanding a
specific value of current. If current exceeds this limit
(due to short circuiting or high voltage fluctuations),
the wire may burn due to excessive heating, and it
may cause a fire. To avoid it , for high voltage and heavy
current, a special wire, called the high tension wire, is
used. A high tension wire has a low resistance and
large surface area. Instead of taking a single thick wire
of low resistance, it is made by twisting together a
number of thin wires insulated from each other so as
to proved a large surface area so that it can radiate the
heat produced more readily as compared to a single
thick wire.
DIRECT CURRENT (DC)
A current which does not change with respect to
time is called direct current.
(ii) AC generator is cheaper than DC generator.
(iii) AC generators are strong and do not require much
attention. The absence of commutator in AC generator
avoids sparkings and increases the efficiency.
(iv) The AC voltage can be easily varied with the help of
a transformer which is a device for changing alternating
voltages. AC voltage can be easily stepped up or down
as per requirement.
(v) AC can be easily converted into DC (if needed) by
means of a rectifier.
DRAWBACKS OF AC
(i) Several chemical processes and effects such as
hydrolysis, electrolysis, electroplating, electro refining
etc., are not at all possible with AC
(ii) AC passes only through the outer layers of the
conductor, unlike DC which passes through whole bulk
of the conductor. Hence, several fine insulated wires
(and not a single thick wire) are required for
transmission of AC.
NTSE STAGE-I_PAGE # 30