Download Reflection: The phenomenon by which the incident light energy is

Ray Optics
Reflection: The phenomenon by which the incident light energy is partially or completely reflected
back into the same medium from which it is coming is called reflection. Reflection can be of two
types
Regular reflection: in regular reflection light is thrown back in well defined direction, thus resulting
in formation of image in the reflecting surface. For e.g. reflection in the case of mirror.
Irregular reflection: The reflection in which the incident energy is not send back in well defined
directions is called irregular reflection. In this case no image formation takes place.
Ray of light: The straight line path along which the light travels in homogenous medium is called
ray of light. A bunch of such rays of light is called beam of light. Beam of light can be of two kinds:
Convergent beam of light: The beam coming from large distance with all the rays of beam
meeting at common point is called convergent beam of light.
Divergent beam of light: The beam of light originating from common point and then moving away
in all possible directions is called divergent beam.
Parallel beam of light: the beam in which all the constituent rays moves parallel to each other is
called parallel beam of light.
Source: All objects which are visible to us are sources of light. However if the source emits light of
its own like in the case of sun or filament bulb it is called self luminous. But if they emit light
obtained from some other source like moon or book near us then they are non luminous sources.
Luminous objects emitting light can be either hot or cold. If the object emtting light is hot the
phenomenon is called incandescence and if cool, like glow worm or TV screen, then it is called
luminescence. In case of luminescence, if the time interval between excitation and emission is less
than 10-8s the phenomenon is called fluorescence and if the time interval is more than 10-8s then it
is called phosphorescence.
Medium: Substance through which light propagates is called medium. The medium can be of three
kinds:
[a] Transparent: the substances for which most of the light propagates through them are called
transparent medium. E.g. water or glass.
[b] Translucent: the medium allow partial propagation of light through them are called translucent
objects. E.g. tracing paper or ground glass etc.
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[c] Opaque: the mediums which don’t allow the propagation of light through them are called opaque
like card board or wood etc.
Object: The object is decided by the incident rays only.
[a]Real object: In this case if the incident rays are diverging, then point of divergence is the
position of real object
[b] Virtual Object; If the incident rays are converging then the point of convergence is position of
the virtual object. We can’t see virtual object by human eye because for object or image to be seen
the rays received by eyes must be diverging.
Image: An image is decided by the reflected or refracted rays only.
[a] Real Image: The image which is formed by actual intersection of reflected or refracted rays. Real
image can be obtained on the screen.
[b] Virtual Image: The image where the reflected rays or refracted rays just appear to converge.
Virtual image can’t be obtained on the screen.
Optical path: it is defined as the distance traveled by the light in vacuum in the same time in which
it travels a given path in the medium. If light travels distance d in medium the time taken is given
by d/v. if the light travels for same time in vacuum, then distance traveled is
X=c
d
 d
v
Which implies distance d travels in medium is equivalent to distance μd in vacuum and optical path
is always greater than the actual path.
Fermat’s Principle: According to this principle if light ray travels from one fixed point to another
fixed point it follows a path that the time taken is optimum[ i.e. either maximum or minimum or
constant]
Laws of reflection: The phenomenon in which the light energy after interacting with the boundary
separating the two mediums comes back in the same medium. In case of reflection, the angle
between incident ray and the normal at point O is called angle
of incidence and the angle between reflected ray and normal at
O is called angle of reflection
According to laws of reflection
[1] the incident ray, reflected ray and the normal ray all lie in
the same plane.
[2] Angle of incidence is always equal to the angle of reflection
i.e. i=r
these laws are true for kinds of reflection taking place either
from plane or the curved surfaces.
Important Points In Reflection
[a] If angle of incidence on the surface is zero, the angle of reflection will also be zero and the ray
will retrace its path.
[b] There is no change in the frequency, wavelength and velocity of the ray after reflection. But the
intensity and thus the amplitude of the wave decreases [ due to some absorption of energy at the
surface or as 100% reflection of energy is not possible]
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[c] Phase change of  or path difference of λ/2 occurs on reflection from the optically denser
medium like air glass boundary but no phase change or path difference occurs if reflection is from
the rarer medium.
Reflection from plane surfaces: Whenever light suffers reflection from the plane surface like a
mirror,
[a] The image formed is always erect, virtual and of same size as that of the object. Its same
distance behind the mirror as object is in front of the mirror.
[b] As every part of the mirror forms complete image of the extended object and due to
superposition of the images brightness will depend on the light reflecting area. Larger the mirror
more bright will be the image formed by the mirror. This also implies that if part of the mirror is
covered with black sheet, image will still be formed but the brightness of the image gets reduced.
Deviation on Reflection: The angle between the directions of the incident and reflected rays of
light is called deviation on reflection As shown in figure, the angle of incidence and reflection are
equal thus the deviation angle is given by
δ=180 -2i
Special Cases: [a] If the angle of incidence is 0 0, then the deviation angle is 1800, which implies that
the ray of light will retrace its path on reflection from the denser medium.
[b] if angle of incidence is 900, then the deviation angle is zero. Such an angle of incidence is called
gracing angle.
[c] If ray of light suffers multiple reflections from mirrors then total deviation in the path of light is
the sum of deviation suffered at each individual reflection.
Spherical mirrors: Spherical mirror is a polished surface which forms the part of the large sphere.
Spherical mirrors can be of two types
[a] Concave mirror: It is spherical mirror which when looked from the reflecting side is depressed
at the center and bulging at the edges.
[b] Convex Mirror: It is spherical mirror which when looked from the reflecting side is bulging
outwards from the center and depressed on the sides.
[c] Pole: The center of the mirror which is most depressed or most bulging out is called the pole of
the mirror.
[d] Center of curvature; the center of the large sphere of which convex or concave mirror is a
small part is called center of curvature.
[e] Radius of curvature: The radius of the curvature is radius of the sphere of which convex or
concave mirror is a part or the distance between the pole of the mirror and its center of curvature.
[f] Principal Axis: A straight line joining the pole of the mirror and its center of curvature is called
principal axis.
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[g] Aperture: The diameter of the circular outline of the mirror is called aperture of the mirror.
[h] Principal Focus: The point on the principal axis where the rays coming parallel to the principal
axis meets or appears to meet is called principal focus.
[i] Focal Plane: The plane passing through the principal focus and perpendicular to the principal
axis is called focal plane.
[j] Focal length: The distance between the pole of the mirror and the principal focus is called focal
length of the mirror.
Sign Conventions: The sign convention we will be using in the this ray optics section are
[a] Pole of the mirror or lens is considered to be the origin of co-ordinate system
[b] All the distances are measured from the pole of the mirror or lens.
[c] The incident rays are assumed to be moving from left to right always.
[d] the distances to the left of pole are taken as negative and distance to the right of pole are taken
as positive.
[e] distances measured upwards and perpendicular to principal axis are positive , while distances
measured downwards are negative.
Relation between radius of curvature and focal length:
Concave Mirror: Consider a spherical mirror of radius of curvature R and focal length f. The
incident ray AM parallel to the principal axis is assumed to be coming from infinity and after
reflection from the mirror at point M converges towards the focus of the mirror.
Also, if the angle of incidence and reflection is θ, then
PFM  2 [as, exterior angle is sum of interior opposite angles]
As, we assume that the angle of incidence and
reflection is small and mirror also has small
aperture, therefore we assume arc PM to be
straight line perpendicular to the principal axis.
MP
CP
MP
Tan 2θ =
FP
Tan θ =
As the angles are small tan θ and tan2θ are
replaced by θ and 2θ respectively.
MP
FP
 MP  MP
2

 CP  FP
CP  2 FP
2 
Convex Mirror: In the case of convex mirror, the incident ray AM moving parallel to the principal
axis after reflection from the mirror bends away from the principal axis and appears to converge at
point F.
Also, if the angle of incidence and
reflection is θ, then
PFM  2 [as, exterior angle is sum
of interior opposite angles]
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As, we assume that the angle of incidence and reflection is small and mirror also has small aperture,
therefore we assume arc PM to be straight line perpendicular to the principal axis.
MP
CP
MP
Tan 2θ =
FP
Tan θ =
As the angles are small tan θ and tan2θ are replaced by θ and 2θ respectively.
MP
FP
 MP  MP
2

 CP  FP
CP  2 FP
2 
Mirror Formula :
Concave Mirror
Assumptions :
The main assumptions while
deriving the mirror formula are :
(a) The aperture of the mirror is
small.
(b) The rays of light makes small
angle with the principal axis.
(c) The object lies on the principal
axis which is horizontal while mirror
is vertical.
Consider an object AB placed in
erect position on the principal axis. The ray BM moving parallel to the principal axis after reflection
passes through focus. Another ray BP is reflected from pole and the two rays meet at B, then AB
is called the image.
Consider ABP & ABP
BAP = BAP = 90
BPA = BPA
Therefore, the two triangles are similar and
AB
AP

A' B' A' P
Similarly BAC and BAC are similar and therefore,
AB
AC

A' B' A' C
From (1) and (2),
AP
AC

A' P A' C
u u R

v  Rv
uR  vR  2uv
Dividing by uvR, we get,
(as i = r)
...( 1)
...( 2)
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1 1 2
 
v u R
1 1 1
 
u v
f
Linear Magnification:
It is the ratio of the size of image to the size of the object.
size of image A' B'
m

size of object
AB
From eq. (1)
m
A' B' A' P ' v


AB
AP
u
Also
1 1 1
 
f v u
Multiplying the equation with u,
u u
 1
f
v
u u 1 u  f


v
f
f
f
m
u f
Multiplying mirror formula with v,
v
v
1 
u
f
v
m  1
f
v f
m
f
Note : A word of caution is necessary while we apply the mirror formula to numerical problems. In
particular problem, the parameters known are substituted with proper sign. No sign is however
attached to unknown parameter.
Refraction :
The phenomenon in which ray of light traveling from one medium to another medium of
different optical density, deviates from its original straight line path is called refraction of light.
When light moves from rarer to denser medium it bends towards the normal and when it moves
from denser to rarer medium it bends away from the normal.
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Refraction of light occurs because the speed of light changes as one moves from one medium to
another. Also, the wavelength of light changes, but frequency and phase of the wave remains
constant on refraction I,e, ni change in phase or frequency occurs.
Laws of Refraction:
First Law [Snell’s Law] The ratio of the sine of angle of
incidence to the sine of angle of refraction is constant for a
pair of media in contact.
This constant is equal to the refractive index of second
medium w.r.t. first medium. The first medium is one in which
incident ray lies and the second medium is one in which the
refractive ray lie. If 1 and  2 denotes the refractive index for
the two mediums then
sin i  2

sin r 1
Second law: the incident ray, refracted ray and normal all three lie in the same plane which is
plane perpendicular to the refracting surface.
Refractive index of the medium can also be explained in terms of the velocity of light in any given
medium. Absolute refractive index of the medium is the ratio of velocity of light in vacuum to the
velocity of light in that medium
=
cair
cmedium

c
v
Also,
v=
c

When the ray of light moves from denser
This implies that the velocity of light decreases if the medium changes  times.
Real and Apparent Depth :
Whenever an object is placed in optically denser medium, like
object O placed at the bottom of the container, the ray of light starting
from object moves from denser to rarer medium and bends away from
normal. Thus a virtual image of the object is formed at I. Then,
distance OA is called real depth and IA is called apparent depth of
object.
Now,
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sin i 
AB
AB
and sin r 
OB
IB
Using Snell’s law,
sin i 1

sin r  2

IB
 1
OB  2
If rarer medium is air, then 1 = 1 and 2 = 
OB

IB
If angles are small then OB  OA and IB  IA

OA
Real depth

IA Apparent depth
The shift in the position which takes place after refraction from the surface is is x= OA-IA
x  OA 
x  h
OA


1
 h1  

 
h
here ‘h’ denotes the real depth of the object.
Refraction through Compound Plate:
Consider a compound plate made of two materials with refractive index b and c (c > b). A
ray of light incident on ray moving from rarer to denser medium bends towards the normal. Using
Snell’s law,
a
b 
sin i1
sin r1
Similarly, at face M1M1 it suffers refraction and using Snell’s law,
sin r1

sin r2
b
c
Finally at surface M2M2 it suffers refraction and comes out parallel to incident ray as all the
refracting surfaces are parallel.
sin r2

sin r1
c
a
Multiply, all three equations,
a
a
b 
b 
b
b
c  ca  1
c 
1
c
a

c
a
Total Internal Reflection:
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This phenomenon is observed when a ray of light moves from denser to rarer medium. When
the angle of incidence in such a case is greater than the critical angle then light would be reflected
back into the same medium and phenomenon is called total internal reflection.
Consider a source of light S situated in denser medium say water. As the rays move from
denser to rarer medium they bends away from the normal. If we go on increasing the angle of
incidence angle of refraction also goes on increasing (according to Snell’s law). At one particular
angle of incidence, angle of refraction becomes 90º. The angle of incidence for which the angle of
refraction is 90º is called critical angle. If angle of incidence is increased further the ray gets totally
reflected back into the same medium instead of refraction. At critical angle, ic, r = 90.
sin i c

sin 90
1
2 
2
1
1
sin i c
Applications of Total Internal Reflection:
1.
Mirage Formation: It is an optical illusion which
takes place in hot countries. The layers of earth
in contact with the earth are hooter and rarer
whereas the upper layers are colder and denser.
When the ray of light moves downwards after
reflection from object like tree it is moving from
denser to rarer medium. The agle of incidence
goes on increasing with refraction are each layer
of atmosphere. For one particular layer the angle
of incidence is greater than critical angle and the
ray of light suffers total internal reflection back in
the upward direction. Thus a virtual and inverted
image of the object is formed on the ground.
These virtual images produces the impression of reflection from water due to atmospheric
disturbance.
2.
3.
Optical Fibres :
Optical fibres consists of several thousand of very long
fibres of the diameter of 10—4 cm, with refractive index 1.7.
The fibres are located with a thin layer of material of lower
refractive index. Light entering from one side undergoes
about 10 - 12 thousand reflections per meter and comes out
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from other end. Optical fibres can be put to number of application ;
(i)
They can be used to transmit high intensity laser light insider the body.
(ii) They can be used in the field of communication in sending video signals from one place to
another.
(iii)
They are used to see images of body parts not clearly visible in X - Rays.
Refraction Through Spherical Surfaces :
A spherical surface is formed if the refracting surface forms the part of a sphere. The surface
is said to be convex if it bulges towards the rarer medium side and it is concave surface if it bulges
towards denser medium side.
Sign Conventions :
The following sign conventions are used for refraction at single surface.
1.
All the distances are measured from pole of spherical surfaces.
2.
The ray of light moves from left to right with pole - the origin of cartesian coordinate system.
The distances to the right of the pole are positive and to the left of the pole are negative.
Assumptions :
1.
The objects are assumed to be point objects lying on the principal axis.
2.
The aperture of spherical surface is small.
3.
Incident and refracted rays makes small angles with principal axis.
Ray of light Moving from Rarer to Denser Medium:
a)
With convex towards rarer (Real Image):
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Consider an object O lying on the principal axis and the incident ray of light starting from O
makes an angle a with the principal axis. Let CA be the normal and incident ray makes angle i with
it. As ray moves from rarer to denser medium it bends towards the normal and the bending is just
sufficient to make the refracted ray meets the principal axis at I. The refracted ray makes angle a
with the principal axis and r with the normal. Using Snell's law,
sin i  2

sin r  1
If angle of incident and refraction are small, then,
sin i  i and sin r  r
i 2


1i   2 r
r 1
Also
i = +
and
r = 
(because exterior angles are equal to interior opposite angles)
1 ( + ) = 2 (  )
2  1 = 1  + 2 
…(1)
As angle ,  and  are small,
AP '
AP '

OP '
OP
AP ' AP '
  tan  

IP '
IP
AP '
AP '
  tan  

CP '
CP
  tan  
(as aperture is small,
OP '  OP , AP'  AP , CP'  CP )
Substituting these values in (1), we obtain,
 2  1  MP1 '  1  MP1    2  MP1 
CP
 2  1
R
 OP 

1
u

 IP 
2
v
Virtual Image:
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In this case incident ray OA moving from rarer to denser bends towards the normal but the
bending is not sufficient to make it move towards principal axis. Thus, a virtual image of object is
formed at I. Using Snell's law,
sin i  2

sin r  1
If the angle of incidence and refraction are small then sin i ~ i and sin r ~ r,
i 2

r 1
Also,

1i   2 r
i = +
and
r = +
(because exterior angles are equal to interior opposite angles)
1 ( + ) = 2 ( + )
(2  1)  = 1   2 
…(1)
Substituting the values of , ,  in (1), we obtain
MP1
 MP ' 
 MP 
 1  1    2  1 
CP
 OP 
 IP 
 2  1


 1  2
R
u v
 2  1
 
 1 2
R
v
u
(  2  1 )
(b) With Concave Towards Rarer Medium:
The ray of light starting from point object O lying on the principal axis moves towards the
normal as it moves from rarer to denser medium and virtual image of the object is formed at I.
Using Snell's law
sin i  2

sin r  1
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If the angle of incidence and refraction are small then sin i ~ i and sin r ~ r,
i 2

r 1

1i   2 r
where
i = 
and
r = 
1 (  ) = 2 ( + )
(2  1)  = 1  + 2 
…(1)
Substituting the values of , ,  in (1), we obtain
(  2  1 )
MP1
 MP ' 
 MP 
  1  1    2  1 
CP
 OP 
 IP 
 2  1
 1  2


R
u v
 2  1


 2  1
R
v
u
Similarly, we can prove the identical results for light moving from denser to rarer medium.
Lens :
A portion of refracting material bound between two spherical surfaces is called lens.
(i)
A lens is said to be converging if the width of the beam decreases after refraction through it.
Focal length of converging lens is taken
as positive.
(ii) A lens is said to diverging if the width of beam increases after refraction through it.
length of diverging lens is negative.
Focal
Definitions Regarding Lenses :
Optical Centre :
It is a point lying on the principal axis of lens within or outside it, such that ray of light passing
through it goes undeviated. If the two surfaces are of same radii of curvature then optical centre
lies exactly in the centre of the lens.
Radius of Curvature (R1 & R2) :
Radius of curvature of a surface of lens is defined as the radius of that sphere of which surface
forms a part.
Principal Axis :
The line joining centre of curvature of two surfaces and passing through optical centre is called
principal axis.
Principal Focus :
Principal focus of the lens is a point at which beam of light coming parallel to the principal axis
actually meets or appears to meet after refraction through lens.
Focal Length :
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Focal lenght of a lens is defined as the distance between focus and optical centre. It is denoted
by f.
Focal Planes :
It is plane passing through the principal focus and perpendicular to principal axis.
Len's Formula :
Lens formula is a relation between focal length of lens with the distance of objects and images.
Convex lens:
Let AB be the object placed on the principal axis and beyond focus F. The ray starting from A
passing through optical centre goes undeviated and the ray moving parallel to principal axis passes
through focus. The two ray meet at A1, then A1B1 is the image of the object AB.
As ABC and A1B1C are similar,
AB
BC

A1 B1 B1C
...(1)
Also, CDF and A1B1F are similar,
CD
CF

A1 B1 FB1
Also, CD = AB =>
AB
CF

A1 B1 FB1
...(2)
From (1) and (2),
BC
CF

B1C FB1
u
f

v
v f
uf  vf  uv
Dividing by uvf,
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1 1 1
 
v u f
Virtual Image:
If the object lies between
optical centre and the principal focus
then a virtual image of the object is
formed. Again as ABC and ABC
are similar.
AB
AC

A1 B1 B1C
...(1)
Similarly, as CDF and ABF are similar
CD
CF

A1 B1 FB1
...(2)
from (1) and (2) and CD = AB,
AC CF

A' C FB1
u
f

v v f
uf  vf  uv
Dividing by uvf,
1 1 1
 
v u f
Linear Magnification:
The linear magnification produced by a lens is the ratio of size of the image to the size of the
object.
m
size of image(A' B' ) A' C

size of object (AB)
AC
m
 h2
v

h1
u
( from (1))
( for real image )
For virtual image,
m
h2  v

h1  u
Thus, for a convex lens, linear magnification is positive when image is virtual and negative if
image is real. Similarly, for concave lens the linear magnification is always positive.
m
h2 v

h1 u
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Lens Maker’s formula:
Consider a thin lens with optical centre C, and the point object O placed on the principal axis of
this lens. Light originating from the object on principal axis after refraction at the first surface
heads towards I1. Refraction takes place at the second surface and final image is formed at I.
Refraction At AP1B :
Consider refraction at first surface only 1,  1 and 1 are the angles which the incident ray,
refracted ray and normal to
the first surface makes with
sin i1  2
the principal axis.
Using


1 sin i1   2 sin i2
sin
r2 1
Snell's Law,
As angle of incidence and refraction are small, therefore, sin i1  i1 and sin r1  r1
1 i1 = 2 r2
Also
i1 = 1 + 1 and r1 = 1   1
1 (1 + 1) = 2 (1  1)
(2  1) 1 = 2  1 + 1 1
…(1)
Refraction at second surface AP2B:
If there is no second surface the refracted ray from first surface meets the principal axis at I1
but in moving from denser to rarer medium refraction takes place at second surface. The ray bends
away from normal to second surface and final image is formed at I2. Using Snell’s law,
1 sin i1 = 2 sin r2
As angle of incidence and refraction are small, therefore, sin i2  i2 and sin r2  r2
2 i2 = 1 r2
Also
2 (2 +  1) = 1 (2 + 2)
(2  1) 2 = 1  2  2 1
…(2)
Adding (1) and (2), we get
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1 1 + 2  2 = (2  1) (1 + 2)
…(3)
If angle 1 ,  2 , 1 and 2 are small,
 1  tan  1 
 2  tan  2 
MP1
OP1
T P2
I 2 P2
MP1
 1  tan  1 
C1 P1
 2  tan  2 
T P2
C 2 P2
Substituting these values in (1), we obtain,
 1
1

1
 2  ( 2   1 )

OC I 2C
 CC1 CC 2
1 1  2  1  1
1

 

v u
 1  R1 R2






 1
1
1 
 ( 1  2  1)


f
 R1 R2 
Similarly, the relation can be proved for concave lens also.
Power of a Lens :
Power of lens is the ability of lens to converge or diverge a beam of light falling on the lens.
Mathematically, it is equal to the reciprocal of focal length.
P
 1
1
1 
 (  1)


f
 R1 R2 
Units of power is Dioptres, if focal length is measured in meters.
The number of lenses can be combined to increase the magnification (compound microscope),
make the final image erect (terrestrial telescope). As each lens has its own magnifying power, the
resultant magnification is the product of magnification of individual lenses i.e.
m = m 1  m 2  . . . . .  mn
and resultant power is
P = P1 + P2 +. . . . . .+ Pn
If we have two lenses with distance d between them, then resultant power is P = P1 + P2 
dP1 P2
Refraction through Prism:
A prism is a wedge shaped body made from refracting medium bound by two plane faces
inclined to each other at same angle. The two plane faces are refracting surfaces and angle between
them is the angle of prism.
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Consider ABC as the prism with AB and AC as the two refracting surfaces. The incident ray PE
meets the refracting face AB at E making an angle of incidence i with normal NN1. As it is moving
from rarer to denser medium it bends towards the normal making an angle r1. Similarly, at second
face it moves from denser to rarer medium making an angle of incidence r2 and angle of refraction e
(or angle of emergence). The angle between incident and refracted ray is called angle of deviation.
 = DEF + DFE
= (i  r1) + (e  r2)  (i + e)  (r1 + r2)
…(1)
Again in quadrilateral AENF,
AEN + AFN = 180º
so
ENF + A = 180º
…(2)
Also in ENF,
r1 + r2 + ENF = 180º …(3)
From (2) and (3)
A = r1 + r3
 = (i + e)  A
…(4)
For prism having small refracting angle A the incident ray makes small angle with prism, thus
angle of refraction is also small. Applying Snell’s law, for refraction at face AB and AC,
sin i =  sin r1
sin c =  sin r2
If the angle of incidence and refraction are small, then i =  r1 and e =  r2
 =  (r1 + r2)  A = (  1) A
Angle of Minimum Deviation:
The minimum deviation value of angle of deviation when ray of
light passes through the prism is called the angle of minimum
deviation. In minimum deviation position,
i = e and r1 = r2
A = r1 + r2 = 2r
(where r1 = r2 = r)
Also,
m = i + e  A
m = 2i  A
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i
m  A
2
Using Snell’s law,

sin i
sin r1
 A  m 
sin

2 


 A
sin 
2
An alternate proof will be done in the class.
Dispersion:
A ray of light while passing through a prism spilts
up into its constituent wavelengths. The phenomenon
is known as dispersion. As the deviation suffered by
violet and red light is different (Cauchy's relation),
therefore, colours of dispersed beam will spread in a
cone of angle v  r. This difference of deviation
produced in violet and red light is called angular
dispersion.
v  r = [(v  1)A]  [(v  1)A] = (v  r)A
…(1)
If deviation suffered by mean light is ,
 = (  1) A
…(2)
(1) and (2) =>
 v   r ( v   r )



(  1)
where  is called the dispersive power of prism.
Dispersive power is thus defined as the ratio of angular dispersion to mean deviation
produced by prism. As v > r , therefore, dispersive power is always positive.
Deviation without Dispersion:
In this case, the ray of white light entering the prism comes out as white light. The angles and
material of prism are so adjusted that the dispersion produced in one prism gets exactly cancelled
out by the other. Such a prism is also called achromatic prism. Consider two prism one of crown
glass and other of flint glass having angles of prism A and A respectively. The refractive indices be
 and  respectively. Dispersion produced in two prisms,
(v  r) + (v  r) = (v  r) A + (v  r) A = 0
(v  r)  + (v  r)  = 0


' 
, A' 
as A 

 1
'1 

  +   = 0
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which is the necessary condition for achromatism. The net deviation produced in the prism is
given by,
D =    = (  1) A + (  1) A
  r 
D  (  1) A  ('1)  v
A  0
  v   r 
   1  v   r 
D  (  1) A 1 

A  0
  1  v   r 



D  (  1) A  1  
 

Dispersion without Deviation:
In this case, incident ray and emergent ray are parallel to each other and emergent ray
consists of rays of various colour in dispersed form. As net deviation produced is zero,
D =  +  = 0
D = (  1)A + (  1) A = 0
A 
A  (  1)

A
 1
(  1) A
or
(  1)
Scattering :
When a beam of white light is passed through a water tank containing few drops of milk, the
color of light when observed at right angles to its propagation is rich in blue. This could be explained
due to scattering.
When a beam of light is incident on particles of very small size, smaller than the order of
wavelength of light, light proceeds in all possible directions. The phenomenon is called scattering.
According to Rayleigh's law " The intensity of scattered light, having wavelength l, varies
inversely as fourth power of its wavelength."
I 
1
4
As r = 2 b, therefore, scattering of blue colour will be 16 times more than that of light.
Blue color of Sky :
Being shorter wavelength, scattered blue light dominates and hence sky appears blue.
Fraunhoffer Lines (Solar Spectrum) :
It has been observed that solar spectrum consists dark lines in the solar spectra. These lines
are called Fraunhoffer lines. Sun consists of three layers with innermost layer called photosphere
with temperature of the order of 20 x 10 6 K. Second layer is the sun's atmosphere which consists of
gases mainly hydrogen and helium. The temperature is very high of the order of thousands of
degree centigrade. The outermost part of the sun is chromosphere with temperature of about
6000ºC. Light emitted from sun's atmosphere consists of continuous spectra. As the light passes
through the chromosphere, various elements present there absorb the wavelengths which they
themselves will emit when hot. This results in appearance of dark lines in the spectra. Fraunhoffer
lines are used to study elements present on sun.
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Simple Microscope:
Object is placed between convex lens and principal
focus an erect, virtual and magnified image is
formed on the same side of the object. In the
figure object AB which when viewed by an unaided
eye cannot be seen distinctly. A convex lens is then
interposed between the eye and the object so that
the distance 'a' of the object from the lens is less
than the focal length of the lens. A virtual, erect
and magnified image A'B' will be produced. By
adjusting the distance of object image is formed at
least distance of distinct vision
Magnifying Power :
It is the ratio of angle subtended by the image at the eye to the angle subtended by the object
at the eye when both are placed at least distance of distinct vision.
 tan 

 tan 
Magnifying Power 
AB
CB' D
 CB 

A1 B ' CB u
CB'
...(1)
Since the virtual image is formed at least distance of distinct vision, therefore, V = D. Using
Lens Formula,
1 1 1
 
v u f
1 1 1
 
D u f
Multiplying both sides by D, we get,
1
D
D

u
f
D
D
 1
u
f
...( 2)
From (1) and (2),
M 1
D
f
Compound Microscope:
It is used where larger magnification is required. The convex lens O of short focal length and
short aperture and eye piece of short focal and large aperature is required.
Let AB be an extended object situated on the principal axis at distance greater than focal
length of the objective. As refraction takes place through the objective O, a real inverted and
magnified image A’B’ is formed. The position of eye piece so adjusted that A’B’ falls within its focal
length and so the final image A’’B’’ is formed at least distance of distinct vision. Thus, final image
A”B” is formed in highly magnified but is inverted with respect to the object AB. The course of rays
forming the final image.
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Magnifying Power:
The magnifying power is defined as the angle subtended by the final image at the eye to the
angle subtended by object when both are placed at least distance of distinct vision from eye.
M 
M 



tan 
tan 
A' ' B' ' ' A' B'

 MO  MC
A' B'
AB
For objective lens,
v
u
Again since the lens E, acts like simple microscope, its magnification MC is given by,
D
MC  1 
fe
MO 
Thus, magnification of compound microscope should be,
v
D
M   1 
u
fe




Astronomical Telescope:
Device used to see very far off heavenly bodies. The objective lens has large focal length and
large aperture. The eye piece has small focal length and small aperture. A parallel beam of light
coming from distance object forms a real, inverted and diminished image at a distance f0 from O.
The image then acts as an object for eye piece, and final image is formed after refraction through
eye piece.
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Normal Adjustment:
If the final image is formed at infinity after refraction through the eye piece. The magnifying
power of telescope is defined as the ratio of angle b subtended by the image to the angle subtended
by the object at the eye when both are placed at infinity.
M 
M 
C1B'  f 0
C2 B '  f e

tan 


tan 
A' B' C1B' C1B'


C2 B' A' B' C2 B'
focal length
focal length
M 
of objective 
of eye piece 
f0
fe
The distance between the two lenses is (f0 + fe).
When image is at least distance of distinct vision:
The objective lens forms the real inverted and diminished image A’B’ at fn.
If A’B’ forms the real image within the focal length fe of the eye piece, a final virtual but
magnified image A”B” is observed. The position of eye piece is so adjusted that final image is
formed at least distance of distinct vision D from the eye.
Magnifying Power:
It is the ratio of angle subtended at the eye by the final image formed at least distance of
distinct vision to the angle subtended by the unaided eye by the object at infinity.
M 

tan 
A' B' C1 B'




tan 
C 2 B' A' B'

f0
C1 B'

C 2 B'
 ue
Using Lens formula,
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1
fe

1
1

v
u
1

u
1
1

fe
D
u 
M 
Q.1
A.1
Q.2
A.2
Q.3
A.3
Q.4
A.4
Q.5
A.5
 fe D
fe  D
f0  fe  D 
f e  D 
What is the cause of refraction when light
passes from one medium to another?
The speed of light is different in different
mediums. The speed is maximum in air or
vacuum. Thus, when light passes from rarer to
denser medium, the speed decreases and it
bends towards normal. When it moves from
denser to rarer medium speed increases and it
bends away from normal.
What will happen if lens is immersed in liquid
of refractive index greater than the refractive
index of glass?
When refractive index of the medium is greater
than the refractive index of the lens the nature
of the lens will change i.e. convex will change
into concave and concave will behave as
convex.
A bird flying high in the air appears to be
higher than that in reality to fish in water.
Explain why?
The bird flying high in the air is in rarer
medium, whereas the fish is in denser
medium. Now the light reflected by bird moves
from rarer to denser medium and bends
towards the normal. Thus virtual image of the
bird is formed at a height greater than the
actual height of the bird.
Air bubble inside water shines brightly why?
Light traveling from water to air inside bubble
suffers total internal reflection at the interface,
which results in bubble appears to shine.
Why does diamond sparkle?
The high refractive index of diamond results in
small critical angle for diamond [ about 240]
Diamond is cut in such a way that light which
enters diamond is not allowed to come out of it
and suffers total internal reflection inside
diamond. Thus it shines.
Q.6
A.6
Q.7
A.7
Q.8
A.8
To fish under water viewing obliquely by a
fisherman standing on the bank of lake, does
the man appear taller or shorter than what he
actually is?
As man is in air, the light travels from rarer to
denser medium and bends towards normal.
Thus virtual image of the of the head is at
larger height than it actually is and man
appears taller.
The refractive index of diamond is much
greater than that of ordinary glass. Is this fact
of some use to diamond cutter?
The large refractive index results in small
critical angle for diamond i.e. about 240.
diamond cutter cuts the faces in such a way
that light moving from diamond to air always
strike the surface at angle greater than critical
angel and gets TIR. Thus the diamond shines.
Watching the sunset or sunrise on beach, one
can see the sun for several minutes after it has
been set or minutes before sunrise. Why?
The light of sun moves from rarer to denser
medium and bends towards the normal. Thus
even if sun is below the horizon its virtual
image can be formed above the horizon for 2
minutes.
Q.9
The surface of sunglasses is curved, yet their
power is zero. Why?
A.9
Both the surfaces of sun glass are curved and
their radii of curvature are equal. Thus power of
the lens is given by
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 1
1 
 R  R 
2 
 1
P = ( - 1) 
Thus, if R1=R2, the power of the lens is zero.
Q.10
A convex lens is held in water.. what change do
you expect in the focal length of the lens?
A.10
If the lens is held in water in place of air, the
focal length of the water increases 4 times. For
e.g. if focal length of the lens in air is 20cm in
water the focal length of the same lens is 80cm
Q.11
A lens immersed in transparent liquid becomes
invisible. Under what conditions does this
happen?
A.11
The lens can become invisible if bending of light
doesn’t take place when light moves from liquid
to lens. This is possible if the refractive index of
the liquid is same as the refractive index of the
glass.
Q.12
Does critical depends upon the wavelength of
light?
A.12
Yes, the critical angle decreases with the
increase in refractive index of the material.
Moreover the refractive index decreases with
increase in wavelength. These two concepts
implies that critical angle increases with the
increase in wavelength of light.
Q.13
A.13
Can light traveling from air to glass suffer total
internal reflection?
No, for total internal reflection to take place, the
light should move from denser to rarer medium.
But when moves from air [rarer] to glass
[denser] it can’t be there.
Q.14
The focal length of an equiconvex lens placed in
air is equal to the radius of curvature of either
face. Is it true?
A.14
Focal length and radius of curvature of lens are
equal if the lens is made of glass having
refractive index of 1.5
Q.15
A convex lens placed in medium in which it
behaves as glass plate. What is the ratio of
refractive index of glass plate to the medium?
A.15
The convex lens will behave as glass plate if no
bending of light takes place as light passes
through lens. This is possible if the refractive
index of medium and lens is same and their ratio
is equal to one.
Q.16
What is the phase difference between incident
and refractive rays as light moves from glass to
air?
A.16
Phase of a wave doesn’t change on refraction
when light moves from glass to air. Thus phase
difference between the two rays is zero.
Q.17
An equiconvex lens is of focal length 15cm is cut
into two equal halves in thickness. What is the
focal length of each half?
A.17
If lens is divided into two equal halves each of
equal thickness, then the focal length of each
half will be double the original focal length. In
this case focal length of each half will be 30cm.
Q.18
How many images of an object will be formed
when the lens is made by joining two parts
[upper and lower] of different focal length?
A.18
The lens whose material above the principal axis
and below axis are different will have two foci
thus two images of the single object be formed.
Q.19
Within a glass slab, a double convex air bubble
is placed. How would the bubble behave?
A.19
This is equivalent to lens of air placed in denser
medium [glass]. Thus it behaves as concave
lens.
Q.20
An object is placed at the focus of the convex
lens. Where will be the image formed?
A.20
if object is placed at first principal focus of the
convex lens its image will be formed at infinity.
Q.21
Write the conditions for total internal reflection to
take place?
A.21
The two essential conditions for total internal
reflection to take place [a]the ray of light should
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25
move from denser to rarer medium [b] the angle
of incidence for the ray should be greater than
the critical angle.
Q.28
the image of the object formed by the lens on
the screen is not in sharp focus. Suggest a
method to get the focusing of the image on the
screen without disturbing the position of the
object, lens or screen?
A.28
Different colours have different wavelengths and
thus lens possess correspondingly different
refractive index and focal length. Thus, to bring
an object in sharp focus we can change the
wavelength of light being used in experiment.
Q.22
Can relative refractive index of medium w.r.t.
another be less than unity?
A.22
yes, the relative refractive index of rarer medium
w.r.t. denser medium is always less than 1. For
e.g. refractive index of glass w.r.t. diamond.
Q.23
Can absolute refractive index of the medium be
less than unity?
Q.29
A stick partially immersed obliquely under water
appears to be bent. Explain, why?
A.23
The absolute refractive index can never be less
than unity, because absolute refractive index is
measured w.r.t. vacuum which has refractive
index 1 and velocity of light is maximum in
vacuum.
A.29
When stick is bent obliquely in water, the
different points on the stick are at different
depths. Since the lateral shift in the position of
the object will be different for different points it
appears to be bent.
Q.24
What are factors on which the lateral shift in the
glass slab depends?
Q.30
How does atmospheric refraction affect the
length of the day?
A.24
It depends upon the thickness of the glass slab
and the refractive index of glass relative to the
medium in which it is placed.
A.30
Q.25
Which of the two parts of optical fiber has higher
value of refractive index?
Due to atmospheric refraction image of sun
appears 2 minutes before sunrise and can be
seen two minutes after sunset. Thus the length
of the day increases by 4 minutes due to
atmospheric refraction.
A.25
The refractive index of fiber material or core of
the optical fiber is more than the refractive index
of coating or cladding of the fiber.
Q.31
How can we explain the phenomenon of the
twinkling of the stars?
A.31
The light from the stars reaches us after
refraction through layers of atmosphere. Thus
the apparent position of star is different from real
position. But because of the variation in
atmospheric layers the apparent position of star
also goes on changing. This will result in
twinkling effect on the star.
Q.32
Can convergent lens in one medium behaves as
divergent lens in another medium?
A.32
Yes, it is possible if the refractive index of the
medium becomes greater than the refractive
index of the lens. Then nature of lens changes.
Thus, convergent lens in air behaves as
divergent lens in the optically denser medium
whose refractive index is greater than that of
lens.
Q.26
Why is power of the lens measured as reciprocal
of focal length of the lens?
A.26
A lens is said to behaving more power if it can
focus the rays of light close to the lens. Thus
larger the power smaller will be focal length of
the lens. Thus, power of the lens is measured as
reciprocal of the focal length.
Q.27
An object is placed at the focus of the concave
lens. Where will the image be formed?
A.27
The virtual image will be formed on the left side
of the lens at infinity.
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Q.33
An empty glass tube appears silvery when
dipped in water and viewed through a particular
angle. Why?
A.33
This happens when the total internal reflection
takes place when rays of light move from the
glass to air. As a result the test tube appears
highly polished.
Q.34
A converging and diverging lens of equal focal
length are placed in contact. Find the resultant
focal length and power.
A.34
The resultant focal length is
1
1 1
  0
fr
f
f
A.38
When white light passes through blue and
yellow filter light will be mainly green with tinge
of blue and yellow in it
Q.39
Why danger signals are red in colour?
A.39
The scattering of light is inversely proportional
to the fourth power of the wavelength, thus as
red colour has maximum wavelength in visible
spectrum, the scattering of red light is
minimum and it can be seen from large
distance.
Q.40
Why sun appears red when at the horizon?
A.40
The scattering of light in inversely proportional
to fourth power of wavelength. Thus when sun
is at the horizon lower wavelengths gets
scattered due to large distance and sun
appears to be red.
Q.41
When does a ray incident on prism deviate
away from the base?
A.41
When the prism is immersed in a liquid whose
refractive index is greater than the refractive
index of prism, the rays after refraction deviate
away from the base of the prism.
Q.42
Explain why white light is dispersed when it
passes through the prism?
A.42
White light consists of different colours and all
having different wavelength and refractive
indices. Thus when white light passes through
the prism different colours suffers deviation
through different angles and light appears to
be dispersed.
Q.43
Why does sky appears blue in the day?
A.43
In the day, the distance of sun from the earth is
minimum, thus scattering of lower wavelengths
is more prominent and the sky appears to be
blue.
Q.44
What is dipsersive power of the prism?
A.44
It is the ratio of the angular dispersion of light
passing through the prism to the deviation
 f r  inf inity
This happens as focal length of converging
lens is f and diverging lens is –f. thus the
resultant power of the lens is zero.
Q.35 Why does lenses with large aperture suffer
from spherical aberration?
A.35 The lenses with large aperture suffers from spherical
aberration because the marginal and paraxial rays
which are moving parallel to the principal axis
converge at different points after refraction through
lens.
Q.36
A lens made of glass is immersed in water, will
its power increase or decrease?
A.36
Power of the lens is reciprocal of focal length.
On immersion in water focal length of the lens
increases about 4 times, thus power of the
lens will decrease 4 times.
Q.37
What are the uses of putting two lenses in
contact with each other?
A.37
Putting two lenses in contact will increase the
magnification of the image and it can also be
used to decrease the spherical aberration in
the lenses.
Q.38
What colour would you observe when white
light passes through blue and yellow filter?
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suffered by mean light [yellow] when it passes
through the prism.
Q.52
How would a blue object appears under yellow
light of sodium vapour lamps?
Q.45
Which photon is more energetic violet or red?
A.52
A.46
As frequency of violet light is more than the
frequency of red light. Thus violet photons are
more energetic [Energy = h]
Blue light appears blue it reflects blue light, but
when yellow light falls it doesn’t reflect any
radiations and the object appears to be black.
Q.53
On what factors does the dipsersive power of
the prism depend?
What is the ratio of speed of infra red to
ultraviolet radiations in air?
A.53
the refractive index of the material of the prism
and the two colours for which the dipsersive
power is to be measured are the factors
affecting the dipsersive power of the prism.
As both are electromagnetic radiations they
will travel with the velocity equal to 3 x 10 8m/s.
thus ratio of their velocities is 1:1
Q.54
What is pure spectrum?
A.54
The spectrum of light in which there is no
overlapping between colours is called pure
spectrum. If the overlapping of colours occurs
it is called impure spectrum.
Q.55
What is the essential conditions for observing
the rainbow?
A.55
rainbow can be observed only if the back of
the observer is towards the sun.
Q.56
What is essential difference between
fluorescence and phosphorescence?
A.54
Fluorescence is the phenomenon of the
instantaneous emission of the energy of lower
frequency after absorption of the radiations of
higher frequency. Phosphorescence is the
phenomenon which occurs with some time
delay i.e. absorption of the radiations and reemitting them after some time.
Q.57
How does the ray of light passes through prism
in position of minimum deviation?
A.57
In position of minimum deviation the path is
symmetrical i.e. angle which incident and
emergent rays makes with the normal must be
equal.
Q.58
Can the image formed by the simple
microscope be projected on screen without
using any additional lens or mirror?
Q.47
A.47
Q.48
Does the materials always have the same
colour when seen through reflected or
transmitted light? Explain.
A.48
No, it is not essential for two colours to be
same because the object may be reflecting
one colour and transmitting another.
Q.49
What does a welder protect against when he
wears a mask?
A.49
A welder protects against the ultraviolet
radiations, which are emitted by the carbon arc
of welding machine. The mask he wears has
uv filter which absorbs uv radiations.
Q.50
People usually prefers coloured dresses during
summer and dark coloured dresses during
winter. Why?
A.50
Light coloured dresses absorbs very little
energy, which falls on them thus saving us
from the heat. In winters dark coloured clothes
will absorb the radiations, which helps us, feel
warm.
Q.51
Does a white light passing through hollow
prism gives spectrum of light?
A.51
NO, hollow prism cannot cause dispersion as
all the colours travel with same speed in the air
inside hollow prism. Thus no angular
dispersion is there.
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A.58
Simple microscope forms image which is
virtual and on the same side of the lens where
object is placed. Thus it can’t be obtained on
screen.
Q.59
Why magnifying glass is held close to the eye
when observing small objects?
A.59
this is done because the angular magnification
of the lens decreases with the increase in
distance between the eye and the lens.
Q.60
What is the difference between binocular and
telescope?
A.60
Binocular uses two lenses as compared to the
telescope that has one lens. Thus binocular
gives us three-dimensional view with the
perception of depth also which is never
possible through telescope.
Q.61
Why should the objective of microscope have
small focal length?
A.61
The magnifying power of microscope is M =
L
fo

d 
1   . Thus in order to have large
fe 

magnification the focal length of objective lens
should be small.
Q.62
On inverting the telescope and seeing from the
objective lens object appears smaller. Why?
A.62
The magnifying power of inverted telescope
will be M = fe/f0, as focal length of the objective
is always greater than the focal length of the
eyepiece thus the magnification becomes less
than one.
Q.63
How will you distinguish between compound
microscope and telescope?
A.63
The objective of the telescope has large
aperture as compared to the eyepiece. But in
case of compound microscope eyepiece if of
large aperture but the difference in apertures is
not very large.
Q.64
Why focal length of the objective lens should
be large?
A.64
The magnifying power of astronomical
telescope is M = fo/fe. Thus by increasing the
focal length of the objective lens we can
increase the magnifying power of the
telescope.
Q.65
On what principle is magnifying lass based?
A.65
it is based on the principle that if the object is
placed between focus and optical center of the
lens, virtual, magnified and erect image will be
formed on the same side of the lens.
Q.66
The diameter of the objective lens of the
telescope is made four times. How will the
intensity of the image changes?
A.66
If we double the diameter of the objective lens,
the area of the objective lens becomes four
times. Thus, the amount of light which enters
the telescope and forms image after refraction
becomes four times. Thus the intensity of
image will be increased 4 times.
Q.67
What is the length of the tube of telescope
which forms final image at infinity?
A.67
The final image will be formed at infinity if the
focus of objective and eyepiece coincides.
Thus the length of telescope is sum of the
focal length of objective and eyepiece.
Q.68
How can we increase [a] magnification [b]
brightness of the image formed by telescope?
A.68
Linear magnification can be increased by
increasing the focal length of the objective lens
and decreasing the focal length of the
eyepiece. The brightness or intensity of the
image formed can be increased by increasing
the aperture of the objective lens.
Q.69
What should be the position of the object
relative to biconvex lens so that it acts as
magnifying glass?
A.69
Lens will acts as magnifying glass, if the object
is placed between the focus and optical center.
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Thus, final image will be erect, magnified and
on same side as the object.
Q.70
Which is natural optical instrument?
A.70
Eye is natural optical instrument as it can
adjust aperture and focusing according to
distance and the intensity of light.
Q.71
An object is seen through red light and then
through violet light in simple microscope. In
which case the magnifying power of simple
microscope greater?
A.71
The
magnifying
power
microscope is M =
of
L
fo
the
simple
A.74
The images in this case can be obtained either
using fluorescent screen or using photographic
plates both of which gets affected by uv
radiations.
Q.75
List some advantages of reflecting telescope?
A.75
There is no chromatic aberration in reflecting
telescope, which implies that all colours
converge at same point, Moreover spherical
aberration can be reduced by using parabolic
reflecting surfaces.
Q.76
Magnifying power of microscope is inversely
proportional to the focal length of the lens.
What then stops us from manufacturing lenses
of smaller and smaller focal length and
increasing magnifying power?
A.76
Smaller focal length lenses are generally
thicker at the center thus dispersion of light
takes place in such an object with different
colour converging at different points [chromatic
aberration] which results in faint multi coloured
images.

d 
1   . Using
fe 

violet light of smaller wavelength the focal
length of both the lens decreases. Thus
increasing the magnifying power of the
microscope.
Q.72
If telescope in inverted, will it work as
microscope?
A.72
No, it is not possible because inverted
telescope forms faint and diminished images.
Q.77
The image of the objective in the eyepiece is
known as eye ring. What is the best position of
our eyes for viewing?
Q.73
Since glass is opaque to ultraviolet light, how
can such a microscope be made?
A.77
A.73
Microscopes in which ultraviolet radiations are
to be used re generally made of quartz or
fluorite, which are transparent to wavelengths
of about 2100A and 1200A respectively.
The image of the objective of the eyepiece is
called eye ring. All the rays refracted by
objective goes through eye ring. When we
position of our eye on the eye ring and area of
the pupil is greater or equal to the area of eye
ring, our eyes will collect all the refracted rays
and image will be maximum intensity.
Q.74
How are images seen if ultraviolet light is used
to increase the magnification?
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