Download optics - einstein classes

PO– 1
OPTICS
Syllabus :
Reflection and refraction of light at plane and
spherical surfaces, mirror formula, Total interanl
reflection and its applications, Deviation and
Dispersion of light by a prism, Lens Formula,
Magnification, Power of a Lens, Combination of
thin lenses in contact, Mircosrope and
Astronomical Telescope (reflecting and refracting)
and their magnifying powers.
Wave optics : wavefront and Huyges’ principle,
Laws of reflection and refraction using Huygen’s
principle. Interference, Young’s double slit
experiment and expression for fringe width,
coherent sources and sustained interference of light.
Diffraction due a single slit, width of central
maximum. Resolving power of microscopes and
astronomical telescopes, Polarisation, plane
polarized light; Brewster’s law, uses of plane
polarized light and Polaroids.
Einstein Classes,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111
PO – 2
CONCEPTS
Ray Optics :
C1
Law of Rectilinear Propagation of Light.
It states that light propagates in straight lines in homogeneous media. It is due to very smaller wavelength
of light
C2
C3
Types of image & types of objects :
(i)
Real image : If reflected (or refracted) rays converge to a point (i.e. intersect there), the point is
a real image.
(ii)
Virtual image : If reflected (or refracted) rays appear to diverge from a point, the point is a
virtual image.
(iii)
Real object : If the incident rays diverge from a point, the point is a real object.
(iv)
Virtual object : If incident rays are appear to converge at a point behind the mirror (or lens), the
point is a virtual object.
Laws of Reflection
(i)
The incident-ray, the reflected-ray and the normal to the reflecting surface at the point of
incidence all lie in the same plane.
(ii)
The angle of reflection (r) is equal to the angle of incidence (i) i.e. i = r.
These laws are applicable to all reflecting surfaces either plane or curved.
C4
Reflection From Plane Surface
(i)
When a real object is placed in front of a plane mirror, the image is always erect, virtual and of same size as
the object. It is at same distance behind the mirror as the object is infront of it.
(ii)
The image formed by a plane mirror suffers lateral-inversion i.e., in the image formed by a plane mirror
left is turned into right and vice-versa with respect to object a shown in the figure.
(iii)
Deviation () is defined as the angle between directions of incident ray and emergent ray.
If a ray is incident at an angle i, then the deviation is given by  = 180 – (i + r) = (180 – 2i)
The deviation is maximum for normal incidence. max = 1800
when i = 0
(iv)
Keeping the incident ray fixed, if the mirror is rotated through an angle , about an axis in the plane of
mirror then the reflected ray rotates through an angle 2.
(v)
If a person of height h wants to see his full image in a plane mirror, the minimum height of the mirror should
be h/2, whatever be the distance of the person from the mirror. The mirror should be placed such that its
upper edge is midway between the head and the eye of the person and the lower edge is midway between
his feet and eye.
(vi)
Number of images of an object in two mirrors inclined to each other at angle  is given by
 k
if k is odd 
360
(n) = 
.
 where k 

k  1 if k is even
Practice Problems :
1.
Plane mirrors A and B are kept at an angle  with respect to each other. Light falls on A, is reflected,
then falls on B and is reflected. The emergent ray is opposite to the incident direction. Then the angle
 is equal to
(a)
300
(b)
450
(c)
600
(d)
900
[Answers : (1) d]
Einstein Classes,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111
PO– 3
C5
Reflection from Curved Surfaces : To calculate the image distance and height of image due to reflection
from curved surface, we will use the following formula
1.
Mirror formula :
1 1 1
 
u v f
2.
Lateral Magnification, m 
v
u
Important Points :
(i)
As focal-length of a spherical mirror f (= R/2) depends only on the radius of mirror and is independent of
wavelength of light and refreactive index of medium. Hence the focal length of a spherical mirror in air or
water and for red or blue light is same. This is also why the image formed by mirrors do not show chromatic
aberration.
(ii)
In case of spherical mirrors if object distance (x1) and image distance (x2) are measured from focus instead
of pole then the relation between x1 and x2 is given by x1x2 = f2. The graph between x1 and x2 is hyperbola.
This result is called ‘Newton’s formula’.
(iii)
In case of spherical mirrors if we plot a graph between (a)
(1/u) and (1/v) the graph will be a straight line with intercept (1/f) . This is shown in figure.
(b)
u and v the graph will be a hyperbola as for u = f; v =  and for u = , v = f. A line u = v will cut
this hyperbola at (2f, 2f). This all shown in figure.
Practice Problems :
1.
An object 5 cm tall is placed 1 m from a concave spherical mirror which has a radius of curvature of
20 cm. The size of the image is
(a)
2.
0.11 cm
(b)
0.50 cm
(c)
0.55 cm
(d)
0.60 cm
A thin rod of length f/3 lies along the axis of a concave mirror of focal length f. One end of its image
touches an end of the rod. The length of the image is
(a)
f
(b)
f/2
(c)
2f
(d)
1.5 f
[Answers : (1) c (2) b]
C6
Refraction :
Laws of Refraction (Snell’s Law)
(i)
The incidence ray, the refracted ray and the normal to the refracting surface at the point of
incidence all lie in the same plane.
(ii)
The ratio of the sines of the angle of incidence (i) and the angle of refraction (r) is a constant
quantity µ for two given media, which is called the refractive index of the second medium with
respect to the first.
sin i
 cons tan t  µ
sin r
When light propagates through a series of layers of different medium as shown in the figure,
Einstein Classes,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111
PO – 4
then the Snell’s law may be written as
µ1sin1 = µ2sin2 = µ3sin3 = µ4sin4 = constant
In general, µsin = constant
Practice Problems :
1.
A beam of monochromatic blue light of wavelength 4200 Å in air travels in water (n = 4/3). Its
wavelength and frequency in water is
(a)
2800 Å , 7.1 ×1014 Hz
(b)
5600 Å, 7.1 ×1014 Hz
(c)
3150 Å , 7.1 ×1014 Hz
(d)
4000 Å, 7.1 ×1014 Hz
[Answers : (1) c]
C7
Apparent shift

1
The apparent shift in the position of the source is s  h  h  h 1   .
 µ
If there are n numbers of slabs with different regractive indices are placed between the observer and the
object, then the total apparent shift is equal to the summation of all the individual shifts.
s = s1 + s2 + .......... + sn
or



1 
1 
1
  h 2  1 
  .....  h n  1 
s  h 1  1 
µ1 
µ2 
µn






If the shift comes out to be positive, the image of the object shifts toward the observer, and vice-versa.
Practice Problems :
1.
A ray of light from a denser medium strikes a rarer medium at angle of incidence i. The reflected and
the refracted rays make an angle of 900 with each other. The angles of reflection and refraction are r
and r  respectively. The critical angle is
(a)
2.
(b)
cos–1 (tan i)
(c)
sin–1 (tan r  )
(d)
tan–1(sin i)
An air bubble inside a glass slab appears to be 6 cm deep when viewed from one side and 4 cm deep
when viewed from the opposite side. The thickness of the slab is
(a)
3.
sin–1(tan r)
10 cm
(b)
6.67 cm
(c)
15 cm
(d)
12 cm
A glass hemisphere of radius 0.04 m and refractive index 1.6 is placed centrally over a cross mark on
a paper (i) with the flat face, and (ii) with the curved face in contact with the paper. In each case the
cross mark is viewed directly from above. The positions of the images will be
(a)
(b)
(c)
(i)
0.04 m from the flat face
(ii)
0.025 m from the flat face
(i)
at the position of the cross mark
(ii)
0.025 m below the flat face
(i)
0.025 m from the flat face
(ii)
0.04 m from the flat face
Einstein Classes,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111
PO– 5
(d)
0.04 m from the highest point of the hemi sphere for both (i) and (ii).
[Answers : (1) c (2) c (3) b]
C8
Important Points :
(i)
When the glass slab of thickness t and refractive index µ is placed in the path of a convergent

1
beam as shown in the figure, then the point of convergence is shifted by s  t 1  
µ


(ii)
When the same glass slab is placed in the path of the divergent beam as shown in figure, then the

1
path of divergence also gets shifted by s  t 1  
µ

C9
Total Internal Reflection and Critical Angle :
Total internal reflection can occur when the light will travel from denser medium to rarer medium and angle
of incidence should be greater than the critical angle. The critical angle is defined as the angle of incidence
at which the angle of refraction will be /2.
1  µ
Applying Snell’s law at the critical angle µ2 sin c = µ1 or  c  sin  1
 µ2



Practice Problems :
1.
A ray of light traveling in glass (µ = 3/2) is incident on a horizontal glass - air surface at the critical
angle C. If a thin layer of water (µ = 4/3) is now poured on the glass air surface, the angle at which the
ray of light emerge into air at the water - air surface is
(a)
2.
40.40
(b)
58.30
(c)
65.20
(d)
900
A point source of light is placed 4 m below the surface of a liquid of refractive index 5/3. The
minimum diameter of a disc, which should be placed over the source, on the surface of the liquid to
cut off all light coming out of water, is
(a)

(b)
6m
(c)
4m
(d)
3m
[Answers : (1) b (2) b]
C10
Prism
(i)
Angle of prism or refracting angle (A) of prism means the angle between the faces on which
light is incident and from which it emerges,
If the faces of a prism on which light is incident and from which it emerges becomes parallel,
angle of prism will be zero and as incident ray will emerge parallel to itself, deviation will also
be zero i.e., the prism will act as a slab.
(ii)
Deviation Produced by a Prism
Einstein Classes,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111
PO – 6
=i+ e–A
The deviation produced by small angle of prism is given by  = A(µ – 1)
(iii)
Minimum deviation
Theory and experiment show that  will be minimum when the angle of incidence equal to the
 A

sin  min

sin i
2



angle of emergence. The refractive index of the prism is given by µ 
sin r
A
sin  
2
Note that if the prism is equilateral or isosceles then the ray inside the prism is parallel to its
base.
(iv)
Maximum deviation
Maximum deviation occurs when the angle of incidence i is maximum (imax = 900)

(v)
max = 90 + e – A
Condition of No Emergence
A ray of light will not emerge out of a prism (whatever be the angle of incidence) if A > 2c, that
is, if µ > cosec(A/2).
(vi)
Condition of Grazing Emergence
If a ray can emerge out of a prism, the value of angle of incidence i for which angle of emergence
e = 900 is called the condition of grazing emergence.
The value of i for grazing emergence is given by i  sin 1 [ (µ 2  1) sin A  cos A ]
Practice Problems :
1.
A ray of light passes through an equilateral prism such that the angle of emergence is equal to the
angle of incidence and each is equal to (3/4)th of the angle of prism. The angle of deviation is
(a)
2.
200
(d)
300
1800 – 3A
(b)
1800 + 2A
(c)
900 – A
(d)
1800 – 2A
A/µ
(b)
A/2µ
(c)
µA
(d)
µ A/2
The angle of a prism is 60 and the refractive index of the material of the prism is 2. The angle of
incidence for minimum deviation is
450
(b)
600
(c)
300
(d)
sin–1(2/3)
If the refracting angle of a prism is 600 and the minimum deviation is 300, then the angle of
incidence is
(a)
6.
(c)
0
(a)
5.
390
A ray of light is incident at angle i on one surface of a prism of small angle A and emerges normally
from the opposite surface. If the refractive index of the material of the prism is µ, the angle of
incidence i is nearly equal to
(a)
4.
(b)
The refracting angle of a prism is A and the refractive index of the material of the prism is cot (A/2).
The angle of minimum deviation is
(a)
3.
450
300
(b)
600
(c)
450
(d)
900
A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3). A light beam
incident normally on the face AB is totally reflected to reach the face BC, if
(a)
sin   8/9
Einstein Classes,
(b)
sin  2/3
(c)
2/3 < sin  < 8/9 (d)
none of these
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111
PO– 7
7.
A ray falls on a prism ABC (AB = BC) and travels as shown in the figure. The minimum refractive
index of the prism material should be
(a)
8.
2
(b)
(c)
3/2
(d)
3
0
A ray of light undergoes deviation of 30 when incident on an equilateral prism of refractive index
2. The angle made by the ray inside the prism with the base of the prism is
(a)
9.
4/3
150
00
(b)
(c)
450
(d)
300
Ray cannot pass through a prism whose refracting angle is A. If the critical angle of the the material
of the prism is C, then
(a)
A < 2C
A  2C
(b)
(c)
AC
(d)
A<C
[Answers : (1) d (2) d (3) c (4) a (5) c (6) a (7) b (8) b (9) b]
C11
Refraction on Curved Surfaces :
General formula for refraction at curved surface is given as :
where
µ 2 µ1 µ 2  µ1


v
u
R
u is the position of the object from the pole
v is the position of the image from the pole
R is the radius of curvature of the surface
µ1 is the refractive index of the medium in which ray is incident
µ2 is the refractive index of the medium in which ray is refracted.
C12
Importan points for the lens :
1 1 1
 
v u f
1.
Lens Formula :
2.
Lateral Magnification, m 
3.
Lensmaker’s formula
4.
Power of Lens
v
u
 1
1  µ2
1 

 
 1 

f  µ1
 R 1 R 2 
Power of a lens is defined as the reciprocal of focal length, where f is measured in metre. If f is
in metre then the power P of the lens in dioptres is given, P 
1
. The unit of power is dioptre.
f
Practice Problems :
1.
An object 15 cm high is placed 10 cm from the optical centre of a thin lens. Its image is formed 25 cm
from the optical centre on the same side of the lens as the object. The height of the image is
(a)
2.5 cm
Einstein Classes,
(b)
0.2 cm
(c)
16.7 cm (d)
37.5 cm
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111
PO – 8
2.
A thin symmetric convex lens of refractive index of the material 1.5 and radius of curvature 0.5 m is
immersed in water of refractive index
(a)
3.
(b)
4.00 m
(c)
2.00 m
(d)
0.02 m
(c)
green light
(d)
red light
Focal length of a convex lens is maximum for
(a)
4.
0.20 m
4
. Its focal length will be
3
blue light
(b)
yellow light
A convex lens of focal length 15 cm is placed on a plane mirror. An object is placed 20 cm from the
lens. The image is formed
(a)
12 cm in front of the mirror
(b)
60 cm behind the mirror
(c)
60 cm in front of the mirror
(d)
30 cm in front of the mirror
[Answers : (1) d (2) c (3) d (4) a]
C13
Equivalent Focal Length of Lens Combination
If n number of lenses of focal lengths f1, f2, f3,....fn are joined together then the equivalent focal length of the
1 1 1
1
combination is given by F  f  f  ....  f
1
2
n
In terms of power p = p1 + p2 + .... + pn
Sign Convention
Focal length of converging lens is taken as positive and that of the diverging lens is taken as negative.
Practice Problems :
1.
A convex lens of focal length 40 cm is in contact with a concave lens of focal length 25 cm. The power
of the combination in dioptres is
(a)
– 1.5
(b)
– 6.5
(c)
+ 6.5
(d)
+ 6.67
[Answers : (1) a]
C14
Equivalent Focal Length of Lens Mirror Combination
The combination acts like a mirror whose equivalent focal length is given by
where
1 2
1
 
F f l fm
fl = focal length of lens and fm = focal length of mirror
Sign Convention
Focal length of converging lens or mirror is positive; and that of diverging lens or mirror is negative.
Practice Problems :
1.
An equiconvex lens of glass (µg = 1.5) of focal length 10 cm is silvered on one side. It will behave
like a
(a)
concave mirror of focal length 10 cm
(b)
convex mirror of focal length 5.0 cm
(c)
concave mirror of focal length 2.5 cm
(d)
convex mirror of focal length 20 cm
[Answers : (1) c]
Einstein Classes,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111
PO– 9
C15
Optical Instruments
1.
Simple microscope : It is a converging lens of small focal length f. The magnification of this microscope
is given by (a) when the image is at the near point (at the distance D = 25 cm from the lens) then the
D
D
. (b) when the image at infinity then magnification is given by
. In both
f
f
cases the nature of the image is virtual, erect and enlarged.
magnification is given by 1 
2.
Compound microscope : It consists of two converging lens, one is objective of smaller focal length (f0)
and an eyepiece of larger focal length (fe). The final image formed is virtual, enlarged and inverted. The
magnification of this microscope is given by (a) when the image is at the near point (at the distance D = 25
 L 
D
cm from the lens) then the magnification is given by   1   . (b) when the image at infinity then
fe 
 f 0 
 L  D 
magnification is given by    . Here L is the length of the tube of compound microscope.
 f 0  f e 
3.
Astronomical telescope : Magnifying power m of a telescope is the ratio of the angle  subtended at the
eye by the image to the angle  subtended at the eye by the object. m 
 f0
 , where f0 and fe are the
 fe
focal lengths of the objective and eyepiece, respectively.
Practice Problems :
1.
2.
An astronomical telescope has an angular magnification of magnitude 5 for distant objects. The
separation between the objective and the eyepiece is 36 cm and the final image is formed at infinity.
The focal length f0 of the objective and fe of the eye piece are
(a)
f0 = 45 cm and fe = – 9 cm
(b)
f0 = 50 cm and fe = 10 cm
(c)
f0 = 7.2 cm and fe = 5 cm
(d)
f0 = 30 cm and fe = 6 cm
Four lenses with focal lengths ± 15 cm and ± 150 cm are being placed for use as a telescopic
objective. The focal length of the lens which produces the largest magnification with a given eyepiece
is
(a)
3.
– 15 cm
(b)
+ 150 cm
(c)
– 150 cm
(d)
+ 15 cm
The magnification produced by the objective lens and the eye lens of a compound microscope are
25 and 6 respectively. The magnifying power of this microscope is
(a)
19
(b)
31
(c)
150
(d)
150
[Answers : (1) d (2) b (3) c]
WAVE OPTICS
C16
Huygen’s Principle
1.
Every point on a wavefront vibrates in same phase with same frequency
2.
Every point on a wavefront acts like a new independent source and sends at a spherical wave, called a
secondary wave.
3.
Wavefronts move in space with the velocity of wave in that medium.
Using the Huygen’s principle we prove the law of refraction and reflection.
Practice Problems :
1.
In Huygen’s wave theory, the locus of all the points in the same state of vibration is called a :
(a)
half period zone (b)
vibrator
(c)
wavefront
(d)
ray
[Answers : (1) c]
Einstein Classes,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111
PO – 10
C17
Coherent Sources and Interference
Two sources are coherent if they have the same frequency and a constant phase difference. In this case, the
total intensity I is not just the sum of individual intensities I1 and I2 due to the two sources but includes an
interference term whose magnitude depends on the phase difference . The resultant test intensity is given
by I  I 1  I 2  2 I 1I 2 cos 

 

Interference term
For incoherent sources I = I1 + I2
Practice Problems :
1.
Interference fringes are obtained due to the interference of waves from two coherent sources of light
with amplitudes a1and a2 (a1 = 2a2). The ratio of the maximum and minimum intensities of light in
the interference pattern is
(a)
2.
(b)
4
(c)
9
(d)

Two coherent monochromatic light beams of intensities I and 4 I are superposed. The maximum and
minimum possible intensities in the resulting beam are
(a)
3.
2
4 I and I
(b)
5 I and 3 I
(c)
9 I and I
(d)
9 I and 3 I
In the Young’s double-slit experiment, the interference pattern is found to have intensity ratio
between bright and dark fringes as 9. This implies that
(a)
the intensities at the screen due to the two slits are 5 units and 4 units respectively.
(b)
the intensities at the screen due to the two slits are 4 units and 1 unit respectively
(c)
the amplitude ratio is 2
(d)
both (b) and (c) are correct
[Answers : (1) c (2) c (3) d]
C18
Important point for Young’s Double Slit Interference Experiment
D
where n = 0, 1, 2,..............
d
(i)
Position of nth maxima from the central maxima y n  n
(ii)
1  D

Position of nth minima from the central maxima is given by y n   n  
2 d

where n = 1, 2, 3,....
(iii)
Fringe Width : It is defined as the distance between two successive maxima or minima  
(iv)
Intensity Distribution : In YDSE, usually the intensities I1 and I2 are equal then
I = 4I0cos2(/2)
D
d
Practice Problems :
1.
In the double-slit experiment, the distance of the second dark fringe from the central line is 3 mm.
The distance of the fourth bright fringe from the central line is
(a)
6 mm
Einstein Classes,
(b)
8 mm
(c)
12 mm
(d)
16 cm
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111
PO– 11
2.
3.
In Young’s experiment, monochromatic light is used to illuminate the two slits and interference
fringes are observed on a screen placed in front of the slits. Now if a thin glass plate is placed normally in the path of the beam coming from one of the slits, then
(a)
the fringes will disappear
(b)
the fringe-width will decrease
(c)
the fringe-width will increase
(d)
there will be no change in the fringe-width
In Young’s double-slit experiment, if L is the distance between the slits and the screen upon which
the interference pattern is observed, x is the average distance between the adjacent fringes and d is
the slit separation, then the wavelength of light is
(a)
4.
5.
6.
(c)
Ld/x
(d)
1/Ldx
do not change at all
(b)
move slightly farther apart
(c)
move slightly closer together
(d)
disappear completely
If a torch is used in place of monochromatic light in Young’s experiment
(a)
fringes will appear as for monochromatic light
(b)
fringes will appear for a moment and then they will disappear
(c)
no fringes will appear
(d)
only bright fringes will appear
For which of the following colours will the fringe-width be minimum in the double-slit experiment ?
violet
(b)
red
(c)
green
(d)
yellow
In a two-slit experiment with monochromatic light, fringes are obtained on a screen placed at some
distance from the slits. If the screen is moved by
5 × 10–2m towards the slits, the change in fringe
–5
width is 3 × 10 m. If the separation between the slits is 10–3 m, the wavelength of light used is
6000 Å
(b)
5000 Å
(c)
4500 Å
(d)
3000 Å
The Young’s double slit experiment light carried out with light of wavelength 5000 Å. The distance
between the slits is 0.2 mm and the screen is at 200 cm from the slits. The central maximum is at
x = 0. The third maximum will be at x equal to
(a)
9.
xL/d
(a)
(a)
8.
(b)
A double-slit interference experiment is set up in a chamber that can be completely evacuated. With
monochromatic light, an interference pattern is observed when the container is open to air. As the
container is evacuated, a careful observer will note that the interference fringes
(a)
7.
xd/L
1.67 cm
(b)
1.5 cm
(c)
0.5 cm
(d)
5.0 cm
In a Young’s experiment, two coherent sources are placed 0.9 mm apart and the fringes are observed
1.0 m away. If the second dark fringe is at a distance of 1 mm from the central fringe, the
wavelength of light used is
(a)
60 × 10–10 cm
(b)
10 × 10–4 cm
(c)
10 × 10–5 cm
(d)
6 × 10–5 cm
[Answers : (1) b (2) d (3) a (4) b (5) c (6) a (7) a (8) b (9) d]
C19
Diffraction : The bending the light around corners or spreading of light into the geometrical shadow of an
obstacle is called diffraction. Sound wave is easily defracted as comapre to light wave.
Single slit diffraction : If the width of the slit is d and  is the angle made by the wave with the direction
of normal to the slit then (a) the condition of minima is given by dsin = n (b) the condition of maxima is
given by dsin = (n + ½ where n = 1, 2, 3.
Angular width of central maxima is
2
2 D
and width of central maxima is
where D is the distance
d
d
between the slit and the screen.
Einstein Classes,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111
PO – 12
Practice Problems :
1.
2.
3.
A diffraction pattern is obtained using a beam of red light. If the red light is replaced by blue light,
then
(a)
the diffraction pattern remains unchanged
(b)
diffraction bands become nattower and crowed together
(c)
bands become broader and farther apart
(d)
bands disappear
To observe diffraction, the size of the obstacle
(a)
should be of the same order as the wavelength
(b)
should be much larger than the wavelength
(c)
has no relation to wavelength
(d)
should be exactly half the wavelength
Light of wavelength 6328 Å is incident normally on a slit having a width of 0.2 mm. The distance of
the screen from the slit is 0.9 m. The angular width of the central maximum is
(a)
4.
0.09 degrees
(b)
0.72 degrees
(c)
0.18 degrees
(d)
0.36 degrees
The beam of light of wavelength 600 nm from a distant source falls on a single slit 1.00 mm wide and
the resulting diffraction pattern is observed on a screen 2 m away. The distance between the first
dark fringes on either side of the central bright fringe is
(a)
1.2 cm
(b)
1.2 mm
(c)
2.4 cm
(d)
2.4 mm
[Answers : (1) b (2) a (3) d (4) d]
C20
Resolving power : The resolving power of an instrument is a measure of its ability to resolve two close
lying points.
1.
Microscope : The limit of resolution of a microscope, i.e., the least distance between two point objects

where  is the wavelength of light, n is the refractive index of
2n sin 
the medium between the point object and the objective, and  is the half angle of the cone of light from the
object. The expression n sin  is called the numberical aperture. The resolving power is 1/d.
which can be distinguished is d 
2.
Telescope : The resolving power of a telescope is the reciprocal of the smallest angular separation (d)
between two distant objects whose images are separated in the telescope. This is given by d 
1.22
a
where a is the aperture of the objective of telescope.
Practice Problems :
1.
To get high resolving power for a telescope, one should use
(a)
objective of large aperture
(b)
objective of large focal length
(c)
eye piece of large focal length
(d)
eye piece of small focal length
[Answers : (1) a]
C21
Polarization : If the vibrations take place equally in all the directions in a plane perpendicular to the
direction of propagation, the wave is called an unpolarized wave. On the other hand, if the vibrations are
limited to just one direction in a plane perpendicular to the direction of propagation, the wave is said to be
polarized.Only transverse wave can be polarized but longitudinal wave cannot be polarized because they
are symmetrical about the direction of propagation.
Malus Law : If the angle between the polarizer and analyzer is  then the intensity I = I0cos2 where I0 is
the maximum intensity and I is the intensity of the polarized light passed through the analyzer.
Polarization by reflection and Brewster’s law : It is found that unpolarized light, on reflection from a
transparent surface, gets polarized. At a particular angle of incidence, called the polarizing angle or Brewster’s
angleip, the reflected ray is completely polarized. It is observed that when light is incident at polarizing
Einstein Classes,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111
PO– 13
angle, the reflected and the refracted rays are perpendicular to each other. It is easy to show that the
refractive index (n) of the medium is related to the polarizing angle as n  tan i p . This is called Brewster’ss
law.
Practice Problems :
1.
2.
Plane polarised light is passed through a polaroid. On viewing through the polaroid we find that
when the polaroid is given one complete rotation about the direction of light
(a)
the intensity of light gradually decreases to zero and remains at zero
(b)
the intensity of light gradually increases to a maximum and remains maximum
(c)
there is no change in the intensity of light
(d)
the intensity of light varies such that it is twice maximum and twice zero
A beam of unpolarized light is passed first through a tourmaline crystal A and then through another
tourmaline crystal B oriented so that its principal plane is parallel to that of A. The intensity of the
emergent light is I. If A is now rotated by 450 in a plane perpendicular to the direction of the incident
ray, the intensity of the emergent light will be
(a)
I/2
(b)
I/2
(c)
I
(d)
I/4
[Answers : (1) d (2) a]
Einstein Classes,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111
PO – 14
INITIAL STEP EXERCISE
1.
2.
3.
4.
5.
6.
7.
8.
9.
Chromatic aberration in a lens is caused by
(a)
reflection
(b)
interference
(c)
diffraction
(d)
dispersion
10.
An achromatic convergent system of focal length
+ 20 cm is made of two lenses (in contact) of
materials having dispersive powers in the ratio
1 : 2. Their focal lengths must be respectively
(a)
10 cm, – 20 cm (b)
20 cm, 10 cm
(c)
– 10 cm, – 20 cm(d)
20 cm, – 10 cm
Let the minimum deviation produced by a given
prism is  and angle of incidence i. Which of the
following graph will represent the variation of 
with i ?
(a)
The length of a telescope is 100 cm and
magnification is 9. The focal length of the objective
and the eyelens are respectively nearly
(a)
90 cm and 10 cm
(b)
85 cm and 15 cm
(c)
80 cm and 20 cm
(d)
95 cm and 5 cm
(b)
A fish in water sees an object which is 24 cm above
the surface of water. The height of the object above
the surface of water that will appear to the fish is
(a)
24 cm
(b)
32 cm
(c)
18 cm
(d)
48 cm
(c)
Image formed by a convex spherical mirror is
(a)
virtual
(b)
real
(c)
enlarged
(d)
inverted
Rays of light strike a horizontal plane mirror at an
angle of 450. The angle at which a second plane
mirror be placed in order that the reflected ray
finally be reflected horizontally from the second
mirror is
(a)
22.50
(b)
450
(c)
600
(d)
750
(d)
11.
Ray optics is valid when characteristic dimensions
are
(a)
of the same order as the wavelength of
light
The effective focal length in Huygen’s eye-piece is
(f is the focal length of each lens)
(b)
much smaller than the wavelength of
light
(a)
2f
(b)
3f
(c)
much larger than the wavelength of light
(c)
3f/2
(d)
3f/4
(d)
of the order of 1 mm.
Light travels through a glass plate of thickness d
with refractive index µ. If c is the velocity of light
in vacuum, the time taken by light to pass through
this thickness of glass plate is
(a)
dµc
(b)
d/µc
A ray of light falls on the surface of a spherical glass
paper-weight making an angle  with the normal
and is refracted in the medium at an angle . The
angle of deviation of the emergent ray from the
direction of the incident ray is
(c)
µd/c
(d)
cµ/d
(a)
( – )
(b)
2( – )
(c)
( – )/2
(d)
( + )
Which of the following form(s) a virtual and erect
image for all positions of the object ?
(a)
concave lens
(b)
concave lens
(c)
convex mirror
(d)
both (b) and (c) are correct
Einstein Classes,
12.
13.
A bird in air looks at a fish vertically below it
inside water. The height of the bird above the
surface of water is h and the depth of the fish
below the surface of water is d. If the refractive
index of water is n, then the distance of the fish as
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111
PO– 15
observed by the bird is
(a)
(c)
14.
15.
h
h
16.
d
n
(b)
2d
n
(d)
h
h
d
n
d
2n
The contrast in the fringes in an interference
pattern depends on
(a)
fringe width
(b)
wavelength
(c)
intensity ratio of the source
(d)
distance between the slits
Which of the following can form the real and
virtual images both for the virtual object ?
(a)
plane mirror only
(b)
converging mirror only
(c)
diverging mirror only
(d)
converging mirror and diverging mirror
both
The Young’s double-slit experiment is performed
with blue light and green light of wavelength
4360 Å and 5460 Å respectively. If X is the distance
of 4th maximum from the central one, then
(a)
X(blue) = X(green)
(b)
X(blue) < X (green)
(c)
X(blue) > (green)
(d)
X(blue) 5460

X(green ) 4360
FINAL STEP EXERCISE
1.
2.
3.
A thin lens has focal length f, and its aperture has
diameter d. It forms an image of intensity I. If the
central part of the aperture, of diameter d/2, is
blocked by an opaque paper, the focal length of the
lens and the intensity of image will become
(a)
f/2, I/2
(b)
f, I/4
The focal length of the objective and the eye-piece
of a compound microscope are 1 cm and 5 cm
respectively. An object placed at a distance of 1.1
cm from the objective has its final image formed at
25 cm from the eye-piece. The distance between the
objective and the eye-piece is
(c)
3f/4, I
(d)
f, 3I/4
(a)
15.17 cm
(b)
25 cm
(c)
10.25 cm
(d)
20 cm
In displacement method, the length of images in
the two positions of the lens between the object and
the screen are 9 cm and 4 cm respectively. The
length of the object must be
(a)
3 cm
(b)
4 cm
(c)
5 cm
(d)
6 cm
White light is used to illuminate the two slits in a
Young’s double-slit experiment. The separation
between the slits is b and the screen is at a distance
d (>> b) from the slits. At a point on the screen
directly in front of one of the slits, certain
wavelengths are missing. One of the missing
wavelength is
(a)
(c)
 = 4b2/d
2
 = b /3d
Einstein Classes,
(b)
 = 2b2/d
(d)
 = 2b2/3d
4.
5.
A lens forms a sharp image on a screen. On
inserting a parallel sided slab of pyrex between the
lens and the screen, it is found necessary to move
the screen through a distance d in order for the
image to be again sharply focussed. If the
refractive index of pyrex is µ, the thickness of the
slab of pyrex is
(a)
µd/(µ + 1)
(b)
µd/(µ – 1)
(c)
µd/(µ + 2)
(d)
µd/(µ – 2)
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111
PO – 16
6.
A short linear object of length b lies along the axis
of a concave mirror of focal length f at a distance u
from the pole. The size of the image is
 f 
b

uf 
(a)
2
 2f 
b

uf 
(c)
7.
 f 
b

uf 
(b)
 f 
b

uf 
(d)
2
Photographs of the ground are taken, from an
aircraft flying at an altitude of 2000 metres, by a
camera with a lens of focal length 50 cm. The size
of the film in the camera is 18 cm x 18 cm. The area
of the ground that can be photographed by this
camera at any one time is
(a)
720 m × 720 m (b)
600 m × 600 m
(c)
500 m × 500 m (d)
none of these
ANSWERS (INITIAL STEP
EXERCISE)
1.
2.
3.
4.
5.
6.
7.
8.
d
a
d
b
a
a
c
c
9.
10.
11.
12.
13.
14.
15.
16.
ANSWERS (FINAL STEP
EXERCISE)
d
d
c
b
a
c
b
c
1.
2.
3.
4.
5.
6.
7.
d
c
c
a
b
d
a
AIEEE ANALYSIS [2002]
1.
2.
3.
If two mirrors are kept at 600 to each other, then
the number of images formed by them is
(a)
5
(b)
6
(c)
7
(d)
8
4.
Which of the following is used in optical fibres ?
An astronomical telescope has a large aperature to
(a)
reduce spherical aberration
(b)
have high resolution
(c)
increase span of observation
(d)
have low dispersion
(a)
Total internal reflection
(b)
Scattering
Electromagnetic waves are transverse in nature is
evident by
(c)
Diffraction
(a)
polarisation
(b)
interference
(d)
Refraction
(c)
reflection
(d)
diffraction
5.
Wavelength of light used is an optical instrument
are 1 = 4000 Å and 2 = 5000 Å, then ratio of their
respective resolving powers (corresponding to 1
and 2) is
(a)
16 : 25
(b)
9:1
(c)
4:5
(d)
5:4
Einstein Classes,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111
PO– 17
AIEEE ANALYSIS [2003]
6.
7.
To get three images of a single object, one should
have two plane mirrors at an angle of
8.
To demonstrate the phenomenon of interference,
we require two sources which emit radiation
(a)
1200
(b)
300
(a)
of different wavelengths
(c)
600
(d)
900
(b)
The image formed by an objective of a compound
microscope is
of the same frequency and having a
definite phase relationship
(c)
of nearly the same frequency
(a)
real and enlarged
(d)
of the same frequency
(b)
virtual and enlarged
(c)
virtual and diminished
(d)
real and diminished
AIEEE ANALYSIS [2004/2005]
9.
A light ray is incident perpendicular to one face of
a 900 prism and is totally internally reflected at the
glass-air surface. If the angle reflection is 450, we
conclude that the refractive index n
12.
The maximum number of possible interference
maxima for slit-separation equal to twice the
wavelength in Young’s doubleslit experiment is
(a)
infinite
(b)
five
(c)
three
(d)
zero
[2004]
13.
(a)
(c)
n
1
2
n
(b)
n
n
2
A plano convex lens of refractive index 1.5 and
radius of curvature 30 cm is silvered at the curved
surface. Now this lens has been used to form the
image of an object. At what distance from this lens
an object be placed in order to have a real image of
the size of the object ?
(a)
20 cm
(b)
30 cm
(c)
60 cm
(d)
80 cm
(a)
sin (n)
(c)
–1
tan (1/n)
(b)
(d)
(c)
hyperbola
(d)
circle
A fish looking up through the water sees the
outside world contained in a circular horizon. If
4
and the fish is
3
(a)
365
(b)
45
(c)
367
(d)
36/7
[2005]
15.
The angle of incidence at which reflected light is
totally polarized for reflection from air to glass
(refractive index n), is
–1
parabola
12 cm below the surface, the radius of this circle in
cm is
[2004]
11.
(b)
the refractive index of water is
[2004]
10.
straight line
[2005]
14.
(d)
(a)
2
1
2
A Young’s double slit experiment uses a
monochromatic source. The shape of the
interference fringes formed on a screen is
Two point white dots are 1 mm apart on a black
paper. They are viewed by eye of pupil diameter 3
mm. Approximately, what is the maximum distance
at which these dots can be resolved by the eye ?
[Take wavelength of light = 500 nm]
(a)
6m
(b)
3m
(c)
5m
(d)
1m
[2005]
–1
sin (1/n)
16.
–1
tan (n)
[2004]
A thin glass (refractive index 1.5) lens has optical
power of –5D in air. It optical power in a liquid
medium with refractive index 1.6 will be
(a)
25 D
(b)
–25D
(c)
1D
(d)
–1D
[2005]
Einstein Classes,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111
PO – 18
17.
If I0 is the intensity of the principle maximum in
the single slit diffraction pattern, then what will be
its intensity when the slit width is doubled ?
(a)
(c)
I0
(b)
2I0
(d)
18.
I0
2
When an unpolarized light of intensity I 0 is
incident on a polarizing sheet, the intensity of the
light which does not get transmitted is
(a)
zero
(b)
I0
(c)
1
I0
2
(d)
1
I0
4
4I0
[2005]
[2005]
AIEEE ANALYSIS [2006]
19.
The refractive index of glass is 1.520 for red light
and 1.525 for blue light. Let D1 and D2 be angles of
minimum deviation for red and blue light
respectively in a prism of this glass. Then,
(a)
D1 can be less than or greater than D2
depending upon the angle of prism
(b)
D1 > D2
(c)
D1 < D2
(d)
D1 = D2
AIEEE ANALYSIS [2007]
20.
In a Young’s double slit experiment the intensity at
21.

( being
6
the wave length of the light used) is I. If I0 denotes
a point where the path-difference is
the maximum intensity,
(a)
3
4
(d)
–20 cm
(d)
+20 cm
3
2
(b)
2
(c)
I
is equal to
I0
1
(c)
Two lenses of power –15 D and +5D are in contact
with each other. The focal length of the
combination is
(a)
+10 cm
(b)
–10 cm
1
2
ANSWERS AIEEE ANALYSIS
1.
8.
15.
a
b
c
2.
9.
16.
a
b
c
Einstein Classes,
3.
10.
17.
d
a
a
4.
11.
18.
b
d
c
5.
12.
19.
a
b
c
6.
13.
20.
d
c
a
7.
14.
21.
a
d
b
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111
PO– 19
TEST YOURSELF
1.
2.
3.
4.
5.
6.
For a prism the refractive index (µ) is related to
wavelength () as µ = A + B/2. The dispersive power
is large if
(a)
A is large
(b)
B is large
(c)
µ is large
(d)
A and µ are large
When a ray is refracted from one medium into
another, the wavelength changes from 6000 Å to
4000 Å. The critical angle for a ray from the second
medium will be
(a)
2
cos 1  
3
(b)
2
sin 1  
3
(c)
3
tan 1  
2
(d)
 2 
sin 1 

 13 
Which one of the following phenomena is used in
optical fibres ?
(a)
scattering
(b)
successive reflections
(c)
refraction
(d)
total internal reflection
How many images will be formed if two mirrors
are fitted on adjacent walls and one mirror on
ceiling ?
(a)
5
(b)
7
(c)
11
(d)
2
Two waves originating from sources S1 and S2
having zero phase difference and common
wavelength  will show completely destructive
interference at a point P is S1P – S2P is
(a)
5
(b)
3/4
(c)
2
(d)
11/2
Interference pattern is obtained on a screen due to
two identical coherent sources of monochromatic
light. The intensity of the central bright fringe is I.
When one of the sources is blocked, the intensity
becomes I0. The intensity in the two situations are
related as
(a)
I = I0
(b)
I = 2I0
(c)
I = 3I0
(d)
I = 4I0
Einstein Classes,
ANSWERS
1.
b
4.
b
2.
b
5.
d
3.
d
6.
d
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111