Assignment A-13

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Quanta Institute LLP

India’s leading platform for Physical Science
CSIR-NET/JRF (PH)
M(PH)
Assignment-13
ELECTRODYNAMICS
Wave Optics
d its Applications, Friction Newton’s laws of
Motion and its Applications, F
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1. Young's double slit experiment is performed using a beam of C60 (fullerene) molecules,
each molecule being made up of 60 carbon atoms. When the slit separation is 50 nm,
fringes are formed on a screen kept at a distance of 1 m from the slits. Now, the
experiment is repeated with C70 molecules with a slit separation of 92.5 nm. The kinetic
energies of both the beams are the same. The position of the 4th bright fringe for C60
will correspond to the 𝑛th bright fringe for C70 . What is the value of 𝑛 (rounded off to
the nearest integer)? [GATE 2023]
(A) 5 (B) 6
(C) 7 (D) 8
2. Different spectral lines of the Balmer series (transitions 𝑛 → 2, with 𝑛 being the
principal quantum number) fall one at a time on a Young's double slit apparatus. The
separation between the slits is 𝑑 and the screen is placed at a constant distance from
the slits. What factor should 𝑑 be multiplied by to maintain a constant fringe width for
various lines, as 𝑛 takes different allowed values? [GATE 2023]
𝑛2 −4 𝑛2 +4
(A) (B)
4𝑛2 4𝑛2
4𝑛2 4𝑛2
(C) 𝑛2 −4 (D) 𝑛2 +4
3. A student sets up Young's double slit experiment with electrons of momentum 𝑝

incident normally on the slits of width 𝑤 separated by distance 𝑑. In order to observe
interference fringes on a screen at a distance 𝐷 from the slits, which of the following
conditions should be satisfied? [GATE 2022]
ℏ 𝐷𝑤 ℏ 𝑑𝑤
(a) 𝑝 > (b) 𝑝 >
𝑑 𝐷
ℏ 𝑑2 ℏ 𝑑2
(c) 𝑝 > (d) 𝑝 >
𝐷 √𝐷𝑤
4. (MSQ) A plane polarized electromagnetic wave propagating in 𝑦 − 𝑧 plane is incident at

the interface of two media at Brewster's angle. Taking 𝑧 = 0 as the boundary between
the two media, the electric field of the reflected wave is given by [GATE 2022]
√3 1
𝐸⃗𝑅 = 𝐴𝑅 cos⁡[𝑘0 { 𝑦 − 𝑧} − 𝜔𝑡] 𝑥ˆ
2 2
then which among the following statements are correct?
𝜋
(a) The angle of refraction is 6
(b) Ratio of permittivity of the medium of refraction (𝜖2 ) with respect to the medium on
𝜖
incidence (𝜖1 ), 𝜖2 = 3
1
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(c) The incident wave can have components of its electric field in 𝑦 − 𝑧 plane
𝜋
(d) The angle of reflection is 6
5. The electric field of an electromagnetic wave is given by 𝐸⃗ = 3sin⁡(𝑘𝑧 − 𝑡)𝑥ˆ + 4cos⁡(𝑘𝑧 −

𝑡)𝑦ˆ. [GATE 2019]
The wave is
4
(a) linearly polarized at an angle tan−1 ⁡(3) from the 𝑥 - axis
3
(b) linearly polarized at an angle tan−1 ⁡(4) from the 𝑥 - axis
(c) elliptically polarized in clockwise direction when seen travelling towards the
observer
(d) elliptically polarized in counter-clockwise direction when seen travelling towards
the observer
𝑚
6. In a set of 𝑁 successive polarizers, the 𝑚th polarizer makes an angle (2𝑁) with the
vertical. A vertically polarized light beam of intensity 𝐼0 is incident on two such sets
with 𝑁 = 𝑁1 and 𝑁 = 𝑁2 , where 𝑁2 > 𝑁1 . Let the intensity of light beams coming out be
𝐼(𝑁1 ) and 𝐼(𝑁2 ), respectively. Which of the following statements is correct about the
two outgoing beams? [GATE 2019]
(a) 𝐼(𝑁2 ) > 𝐼(𝑁1 ); the polarization in each case is vertical
(b) 𝐼(𝑁2 ) < 𝐼(𝑁1 ); the polarization in each case is vertical
(c) 𝐼(𝑁2 ) > 𝐼(𝑁1 ); the polarization in each case is horizontal
(d) 𝐼(𝑁2 ) < 𝐼(𝑁1 ); the polarization in each case is horizontal
7. A quarter wave plate introduces a path difference of /4 between the two components of
polarization parallel and perpendicular to the optic axis. An electromagnetic wave with
𝐸⃗ = (𝑥ˆ + 𝑦ˆ)𝐸0 𝑒 (𝑘𝑧−𝑡) is incident normally on a quarter wave plate which has its optic
axis making an angle 135∘ with the 𝑋 - axis as shown. [GATE 2018]
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The emergent electromagnetic wave would be

(a) elliptically polarized
(b) circularly polarized
(c) linearly polarized with polarization as that of incident wave
(d) linearly polarized but with polarization at 90∘ to that of the incident wave
8. (NAT) In a Young's double slit experiment using light, the apparatus has two slits of
unequal widths. When only slit-1 is open, the maximum observed intensity on the
screen is 4𝐼0 . When only slit-2 is open, the maximum observed intensity is 𝐼0 . When
both the slits are open, an interference pattern appears on the screen. The ratio of the
intensity of the principal maximum to that of the nearest minimum is_____________
[GATE 2016]
9. A monochromatic plane wave (wavelength = 600 nm)𝐸0 exp⁡[𝑖(𝑘𝑧 − 𝜔𝑡)] is incident

⃗ 1 ⋅ 𝑟 − 𝜔𝑡)] in the
normally on a diffraction grating giving rise to a plane wave 𝐸1 exp⁡[𝑖(𝑘
⃗ 1 | [1 𝑥ˆ + √3 𝑧ˆ]. The period (in 𝜇𝑚 ) of
⃗ 1 = |𝑘
first order of diffraction. Here 𝐸1 < 𝐸0 and 𝑘 2 2
the diffraction grating is ______ (upto one decimal place) [GATE 2015]
10. A plane wave (𝑥ˆ + 𝑖𝑦ˆ)𝐸0 exp⁡[𝑖(𝑘𝑧 − 𝜔𝑡)] after passing through an optical element
emerges as (𝑥ˆ − 𝑖𝑦ˆ)𝐸0 exp⁡[𝑖(𝑘𝑧 − 𝜔𝑡)], where 𝑘 and 𝜔 are the wavevector and the
angular frequency, respectively. The optical element is a [GATE 2015]
(a) Quarter wave plate (b) Half wave plate
(c) Polarizer (d) Faraday rotator
11. In an interference pattern formed by two coherent sources, the maximum and
minimum intensities are 9𝐼0 and 𝐼0 respectively. The intensities of the individual wave
are [GATE 2014]
(a) 3𝐼0 and 𝐼0 (b) 4𝐼0 and 𝐼0
(c) 5𝐼0 and 4𝐼0 (d) 9𝐼0 and 𝐼0
12. Interference fringes are seen at an observation plane 𝑧 = 0, by the superposition of two
plane waves 𝐴1 exp⁡[𝑖(𝑘 ⃗ 1 ⋅ 𝑟 − 𝜔𝑡)] and 𝐴2 exp⁡[𝑖(𝑘
⃗ 2 ⋅ 𝑟 − 𝜔𝑡)], where 𝐴1 and 𝐴2 are real
amplitudes. The condition for interference maximum is [GATE 2013]
⃗1 −𝑘
(a) (𝑘 ⃗ 2 ) ⋅ 𝑟 = (2𝑚 + 1)𝜋
⃗1 −𝑘
(b) (𝑘 ⃗ 2 ) ⋅ 𝑟 = 2𝑚𝜋
⃗1 +𝑘
(c) (𝑘 ⃗ 2 ) ⋅ 𝑟 = (2𝑚 + 1)𝜋
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⃗1 +𝑘
(d) (𝑘 ⃗ 2 ) ⋅ 𝑟 = 2𝑚𝜋
13. A charged particle moves uniformly on the 𝑥𝑦-plane along a circle of radius a centered
at the origin. A detector is put at a distance d on the x axis is to detect the
electromagnetic wave radiated by the particle along the x direction. If 𝑑 ≫ 𝑎, the wave
received by detector is [CSIR JUNE 2023]
(a) unpolarized
(b) circularly polarized with the plane of polarization being the yz-plane
(c) linearly polarized along the 𝑦-direction
(d) linearly polarized along the 𝑧-direction
14. The angular width 𝜃 of a distant star can be measured by the Michelson radiofrequency
stellar interferometer (as shown in the figure below).
The distance ℎ between the reflectors 𝑀1 and 𝑀2 (assumed to be much larger than the
aperture of the lens), is increased till the interference fringes (at P0 , P on the plane as
shown) vanish for the first time. This happens for ℎ = 3 m for a star which emits
radiowaves of wavelength 2.7 cm. The measured value of 𝜃 (in degrees) is closest to
[CSIR JUNE 2023]
(a) 1.0 .63 (b) 2.0 .32
(c) 3.0 .52 (d) 4.0 .26
15. A laser beam propagates from fiber 1 to fiber 2 in a cavity made up of two optical fibers
(as shown in the figure). The loss factor of fiber 2 is 10 dB/km.
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If 𝐸2 (𝑑) denotes the magnitude of the electric field in fiber 2 at a distance 𝑑 from the
𝐸 (0)
interface, the ratio 𝐸2(𝑑) for 𝑑 = 10 km, is [CSIR JUNE 2021]
2
(a) 102 (b) 103
(c) 105 (d) 107
16. The following figure shows the intensity of the interference pattern in the Young's
double-slit experiment with two slits of equal width is observed on a distant screen
If the separation between the slits is doubled and the width of each of the slits is halved,
then the new interference pattern is best represented by [CSIR JUNE 2020]
17. Two coherent plane electromagnetic waves of wavelength 0.5𝜇m (both have the same
amplitude and are linearly polarized along the 𝑧-direction) fall on the 𝑦 = 0 plane.
Their wave vectors 𝑘1 and 𝑘1 are as shown in the figure
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If the angle 𝜃 is 30∘ , the fringe spacing of the interference pattern produced on the
plane is [CSIR JUNE 2019]
(a) 1.0𝜇m (b) 0.29𝜇m
(c) 0.58𝜇m (d) 0.5𝜇m
18. A monochromatic and linearly polarized light is used in a Young's double slit
experiment. A linear polarizer, whose pass axis is at an angle 45∘ to the polarization of
the incident wave, is placed in front of one of the slits. If 𝐼max and 𝐼min , respectively,
denote the maximum and minimum intensities of the interference pattern on the
𝐼 −𝐼
screen, the visibility, defined as the ratio 𝐼max +𝐼min, is [CSIR DEC 2018]
max min
√2 2
(a) (b)
3 3
2√2 2
(c) (d) √3
3
19. The following configuration of three identical narrow slits are illuminated by
monochromatic light of wavelength 𝜆 (as shown in the figure below). The intensity is
measured at an angle 𝜃 (where 𝜃 is the angle with the incident beam) at a large distance
2𝜋𝑑
from the slits. If 𝛿 = sin⁡𝜃, the intensity is proportional to [CSIR JUNE 2018]
𝜆
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(a) 2cos⁡𝛿 + 2cos⁡2𝛿

1
(b) 3 + 𝛿2 sin2 ⁡3𝛿
(c) 3 + 2cos⁡𝛿 + 2cos⁡2𝛿 + 2cos⁡3𝛿
1
(d) 2 + 𝛿2 sin2 ⁡3𝛿
20. The figure describes the arrangement of slits and screens in a Young's double slit
experiment. The width of the slit in 𝑆1 is 𝑎 and the slits in 𝑆2 are of negligible width.
If the wavelength of the light is 𝜆, the value of 𝑑 for which the screen would be dark is
[CSIR JUNE 2017]
𝑎 2 𝑏 𝑎 2
(a) 𝑏√( ) − 1 (b) √( ) − 1
𝜆 2 𝜆
𝑎 𝑏 2 𝑎𝑏
(c) 2 (𝜆) (d) 𝜆
21. A pair of parallel glass plates separated by a distance 𝑑 is illuminated by white light as
shown in the figure below. Also shown in the graph of the intensity of the reflected light
𝐼 as a function of the wavelength 𝜆 recorded by a spectrometer.
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Assuming that the interference takes place only between light reflected by the bottom
surface of the top plate and the top surface of bottom plate, the distance 𝑑 is closest to
[CSIR DEC 2016]
(a) 12𝜇m (b) 24𝜇𝑚
(c) 60𝜇𝑚 (d) 120𝜇m
22. A screen has two slits, each of width 𝑤 with their centres at a distance 2𝑤 apart. It is
illuminated by a monochromatic plane wave travelling along the 𝑥-axis. The intensity of
𝑛𝜆
the interference pattern, measured on a distant screen, at an angle 𝜃 = to the 𝑥-axis
𝑤
is [CSIR DEC 2016]
(a) Zero for 𝑛 = 1,2,3 …

(b) Maximum for 𝑛 = 1,2,3 …
1 3 5
(c) Maximum for 𝑛 = 2 , 2 , 2 …
(d) Zero for 𝑛 = 0 only
23. A parallel beam of light of wavelength 𝜆 is incident normally on a thin polymer film
with air on both sides. If the film has a refractive index 𝑛 > 1, then second-order bright
fringes can be observed in reflection when the thickness of the film is [CSIR DEC 2014]
(a) 𝜆/4𝑛 (b) 𝜆/2𝑛
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(c) 3𝜆/4𝑛 (d) 𝜆/𝑛
24. A double slit interference experiment uses a laser emitting light of two adjacent
frequencies 𝑣1 and 𝑣2 ⁡(𝑣1 < 𝑣2 ). The minimum path difference between the interfering
beams for which the interference pattern disappears is [CSIR JUNE 2014]
𝑐 𝑐
(a) 𝑣 +𝑣 (b) 𝑣 −𝑣
2 1 2 1
𝑐 𝑐
(c) 2(𝑣 (d) 2(𝑣
2 −𝑣1 ) 2 +𝑣1 )
25. An electromagnetic wave is incident on a water-air interface. The phase of the

perpendicular component of the electric field, 𝐸⊥ , of the reflected wave into the water is
found to remain the same for all angles of incidence. The phase of the magnetic field 𝐻
[CSIR JUNE 2012]
(a) does not change (b) changes by 3𝜋/2
(c) changes by 𝜋/2 (d) changes by 𝜋
26. In a Young's double slit interference experiment, the slits are at a distance 2𝐿 from each
other and the screen is at a distance 𝐷 from the slits. If a glass slab of refractive index 𝜇
and thickness 𝑑 is placed in the path of one of the beams, the minimum value of 𝑑 for
the central fringe to be dark is [CSIR DEC 2011]
𝜆𝐷 𝜆𝐷
(a) (b)
(𝜇−1)√𝐷2 +𝐿2 (𝜇−1)𝐿
𝜆 𝜆
(c) (𝜇−1) (d) 2(𝜇−1)
27. Consider three polarizer's 𝑃1 , 𝑃2 and 𝑃3 placed along an axis as shown in the figure.
The pass axis of 𝑃1 and 𝑃3 are at right angles to each other while the pass axis of 𝑃2
makes an angle 𝜃 with that of 𝑃1 . A beam of unpolarized light of intensity 𝐼0 is incident
on 𝑃1 as shown. The intensity of light emerging from 𝑃3 is [CSIR DEC 2011]
𝐼0
(a) 0 (b) 2
𝐼0 2 𝐼0
(c) sin ⁡2𝜃 (d) sin2 ⁡2𝜃
8 4
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28. Circularly polarized light with intensity 𝐼0 is incident normally on a glass prism as
shown in the figure. The index of refraction of glass is 1.5. The intensity 𝐼 of light
emerging from the prism is [CSIR JUNE 2011]
(a) 𝐼0 (b) 0.96𝐼0

(c) 0.92𝐼0 (d) 0.88𝐼0
29. Consider an electron double slit experiment as shown in the figure below, with slits S1
and S2 .
If now, within the shaded region marked 𝐶, a constant uniform magnetic field
pointing outside the page is tumed on, the fringe pattern [TIFR 2023]
(a) will get shifted.
(b) will disappear.
(c) will remain unchanged.
(d) will become dimmer.
30. (MSQ) The following Fraunhofer diffraction pattern was observed in an experiment.
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The aperture arrangement that would yield such a fringe pattern is [TIFR 2023]
(a) (b)
(c) (d)
31. A diffraction grating spectrograph is used to resolve the two sodium D lines (589 and
589.6 nm ) in the first order of diffraction. If the width of the grating is 2 cm and the
focal length of the spectrograph camera is 20 cm, what the linear separation at the focal
plane of the two 𝐷 lines will be about [TIFR 2023]
(a) 6𝜇m (b) 6 mm
(c) 60𝜇m (d) 60 nm
32. The lower half of a single slit of width 𝑑 is covered with a half-wave plate 𝑃 as shown in
the figure below.
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As a result, a beam of coherent monochromatic light of wave vector 𝑘 = 2𝜋/𝜆

incident on the single slit, transmits with an amplitude [TIFR 2021]
1 for 0 < 𝑥 ≤ 𝑑/2
𝑇(𝑥) = {−1 for − 𝑑/2 < 𝑥 ≤ 0
0 otherwise
and a Fraunhofer diffraction pattern is formed on a screen S placed parallel to the slit.
The intensity at a point on the screen at an angle 𝜃 measured from the centre of the slit
(see figure), is proportional to
1 1
(a) Φ2 sin2 ⁡Φ where Φ = 2 𝑘𝑑sin⁡𝜃
1
(b) Φ2 sin4 ⁡Φ where Φ = 𝑘𝑑tan⁡𝜃
1
(c) 𝜙 sin⁡Φ where 𝜙 = 𝑘𝑑cos⁡𝜃
1 1
(d) Φ2 cos 2 ⁡𝜙 where Φ = 2 𝑘𝑑sin⁡𝜃
33. The sketch below shows a radio an internal located at the edge of a calm lake, which has
a receiver 𝑅 at the centre of the dish at a height 𝑎/2 above the ground. This is picking up
a signal from a distance radio-emitting star which is just rising above the horizon.
However, the receiver also picks up a reflected signal from the surface of the lake, which,
at the relevant radio-wavelength, may be taken to be a plane.
If the instantaneous angle of the star above the horizon is denoted 𝛼, thc receiver 𝑅
will detect the first interference maximum when 𝛼 = [TIFR 2018]
𝜆 113 𝜆 113
(a) arcsin⁡ (𝑎) (b) arcsin⁡ (2𝑎)
𝜆 𝜆
(c)arcsin 𝑎 (d)arcsin 2𝑎
34. Light passes through a narrow slit and gives the Fraunhofer diffraction pattern shown
in the adjacent figure.
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Which of the following could be the shape of the slit? [TIFR 2017]
35. A glass plate 𝑃 (refractive index 𝑛𝑃 = 1.54) is coated with a dielectric material 𝐶 with the
refractive index 𝑛𝑐 = 1.6. In⁡order to have enhanced reflection from this coated glass for
near-normal incident light of wavelength 𝜆, the thickness of the coating material 𝐶 must
be [TIFR 2014]
(a) even multiples of 𝜆/2𝑛𝑐 (b) even multiples of 𝜆/4𝑛𝑐
(c) odd multiples of 𝜆/4𝑛𝑐 (d) integral multiple of 𝜆/4𝑛𝑐
36. A cross-shaped opening is illuminated by a parallel beam of white light. A thin plano-
convex cylindrical glass lens is placed 20 cm in front of it, as shown in the figure below.
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The radius of curvature of the curved surface of the lens is 5 cm and 1.5 is the
refractive index of glass. On a screen placed as shown at the plane where a real
image forms on the other side of the lens, the image of the opening will appear as
[TIFR 2013]
37. The Michelson interferometer in the figure below can be used to study properties of
light emitted by distant sources.
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A source 𝑆1 when at rest, is known to emit light of wavelength 632.8 𝑛𝑚. In this case,
if the Movable mirror is translated through a distance 𝑑, it is seen that 99,656
interference fringes pass across the Photo-Detector. For another Source 𝑆2 , moving
at an uniform speed of 1.5 × 107 𝑚𝑠 −1 towards the interferometer along the straight
line joining it to the beam Splitter, one sees 100,068 interference fringes pass across
the Photo-Detector for the same displacement 𝑑 of the Movable Mirror. It follows that
𝑆2 , in its own rest frame, must be emitting light of wavelength. [TIFR 2011]
(a) 661.9 𝑛𝑚 (b) 662.8 𝑛𝑚 (c) 598.9 𝑛𝑚 (d) 631.2 𝑛𝑚
(e) 599.6 𝑛𝑚 (f) 628.0 𝑛𝑚
38. A narrow beam of light of wavelength 589.3 nm from a sodium lamp is incident normally
on a diffraction grating of transmission type. If the grating constant is 1000000 𝑚−1, the
number of principal maxima observed in the transmitted light will be [TIFR 2011]
(a) 7 (b) 5
(c) 3 (d) 1
39. Coherent monochromatic light falling through a small aperture produced a Fraunhofer
diffraction pattern as shown below
By looking at this diffraction pattern carefully one can guess that the shape of the
aperture was [TIFR 2010]
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(a) (b)
(c) (d)
40. Two linear polarizers are placed coaxially with the transmission axis of the first
polarizer in the vertical orientation and the second polarizer in the horizontal
orientation. A half waveplate placed coaxially between these crossed polarizers is
rotating about its axis at an angular frequency 𝜔. At 𝑡 = 0, the fast axis of the half
waveplate was oriented vertically. A beam of unpolarized light of intensity 𝐼0 is incident
along the axis of this optical system. The output intensity measured by a detector after
the beam passes through this optical system is [JEST 2023]
𝐼0 𝐼0
(a) 4 [1 + cos⁡(𝜔𝑡)] (b) 4 [1 − cos⁡(2𝜔𝑡)]
𝐼0 𝐼0
(c) [1 − cos⁡(4𝜔𝑡)] (d) [1 − cos⁡(𝜔𝑡)]
4 2
41. A pair of crossed ideal linear polarizers allow no light to pass through. To produce some
output one can insert optical elements between the crossed polarizers. For given light
beam of input intensity 𝐼0 , Nirmalya inserts a quarter-wave plate between the crossed
polarizers and records an output intensity 𝛼𝐼0 . On the other hand, Ayan inserts two
linear polarizers having orientations 30∘ and 60∘ w.r.t. the first polarizer of the crossed
𝛼
pair, and records an output intensity of 𝛽𝐼∘ . What is the ratio 𝛽 ? [JEST 2022]
42. A thin film surrounded by air has an index of refraction of 1.4. A region of the film
appears bright blue (𝜆 = 400 nm) when white light is incident perpendicular to the
surface. What might be the minimum thickness of the film? [JEST 2022]
A. 140 nm B. 280 nm
C. 420 nm D. 70 nm
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43. A flat soap film has a uniform thickness of 510 nm. White light (having wavelengths in
the range of about 390 − 700 nm ) is incident normally on the film. If the refractive
index of the soap is 1.33, what will be the dominant colour of the reflected light?
(a)Violet (b) Green [JEST 2021]
(c) Red (d) White
44. An ideal polariser is placed in between two crossed polarisers in a coaxial geometry as
shown. The middle polariser is rotated at the angular speed of 𝜔 about the common
axis. If unpolarized light of intensity 𝐼0 is incident on this system, the emergent
intensity of the light would be [JEST
2021]
𝑙0 𝑙0
(a) [1 − cos⁡4𝜔𝑡] (b) [1 − cos⁡4𝜔𝑡]
8 16
𝑙0 𝑙0 1
(c) 16 [1 − cos⁡𝜔𝑡] (d) 16 [1 − 2 cos⁡𝜔𝑡]
45. Three polarizers are stacked, normal to a central axis, along which is incident a beam of
unpolarized light of intensity 𝐼0 . The first and the third polarizers are perpendicular to
each other and the middle polarizer is rotated at an angular frequency 𝜔 about the
central axis (light beam). The time-dependent intensity of light emerging after the third
polarizer will be given by [JEST 2020]
𝐼 𝐼
(a) 𝐼(𝑡) = (160 ) {1 − cos(4𝜔𝑡)} (b) 𝐼(𝑡) = ( 80 ) {1 − cos(2𝜔𝑡)}
𝐼 𝐼
(c) 𝐼(𝑡) = ( 40 ) {1 − 2 cos 𝜔𝑡} (d) 𝐼(𝑡) = ( 20 ) cos 2 𝜔𝑡
46. In Young's double slit experiment (screen distance 𝐷 = 50 cm and 𝑑 = 0.1 cm ), a thin
mica sheet of refractive index 𝑛 = 1.5 is introduced in the path of one of the beams. If
the central fringe gets shifted by 0.2 , what is the thickness (in micrometer) of the mica
sheet? [JEST 2019]
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47. The refractive index (𝑛) of the entire environment around a double slit interference
setup is changed from 𝑛 = 1 to 𝑛 = 2. Which one of the following statements is correct
about the change in the interference pattern? [JEST 2019]
(a) The fringe pattern disappears
(b) The central bright maximum turns dark, i.e. becomes a minimum
(c) Fringe width of the pattern increases by a factor 2
(d) Fringe width of the pattern decreases by a factor 2
48. A collimated white light source illuminates the slits of a double-slit interference setup
and forms the interference pattern on a screen. If one slit is covered with a blue filter,
which one of the following statements is correct? [JEST 2019]
(a) No interference pattern is observed after the slit is covered with the blue filter
(b) Interference pattern remains unchanged with and without the blue filter
(c) A blue interference pattern is observed
(d) The central maximum is blue with colored higher-order maxima
49. An optical line of wavelength 5000Å in the spectrum of light from a star is found to be
red-shifted by an amount of 2Å. Let 𝑣 be the velocity at which the star is receding.
𝑐
Ignoring relativistic effects, what is the value of 𝑉 ? [JEST 2019]
50. A thin air film of thickness 𝑑 is formed in a glass medium. For normal incidence, the
condition for constructive interference in the reflected beam is (in terms of wavelength 𝜆
and integer 𝑚 = 1,2,……) [JEST 2017]
(a) 2𝑑 = (𝑚 − 1/2)𝜆 (b) 2𝑑 = 𝑚𝜆
(c) 2𝑑 = (𝑚 − 1)𝜆 (d) 2𝜆 = (𝑚 − 1/2)𝑑
51. Circular fringes are obtained with a Michelson interferometer using 600𝑛𝑚 laser light.
What minimum displacement of one mirror make the central fringe from bright to dark?
[JEST 2016]
(a) 600 𝑛𝑚 (b) 30 𝑛𝑚
(c) 150 𝑛𝑚 (d) 120 Å
52. Let 𝜆 be the wavelength of incident light. The diffraction pattern of a circular aperture of
dimension 𝑟0 will transform from Fresnel to Fraunhofer regime if the screen distance 𝑧
is, [JEST 2015]
2 2
(a) 𝑧 ≫ 𝑟0 /𝜆 (b) 𝑧 ≫ 𝜆 /𝑟0
2
(c) 𝑧 ≪ 𝜆 /𝑟0 (d) 𝑧 ≪ 𝑟02 /𝜆
53. The resolving power of a grating Spectro graph can be improved by [JEST 2014]
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(a) recording the spectrum in the lowest order

(b) using a grating with longer grating period
(c) masking a part of the grating surface.
(d) illuminating the grating to the maximum possible extent.
54. When unpolarized light is incident on a glass plate at a particular angle, it is observed
that the reflected beam is linearly polarized. What is the angle of the refracted beam with
respect to the surface normal? The refractive index of glass is 1.52 [JEST 2012]
𝑜 𝑜 𝑜
(a) 56. 7 (b) 33. 4 (c)23. 3
(d) The light is completely reflected and there is no refracted beam.
55. Diffraction of light can be exhibited by light with an obstacle having dimension of the
order of
(a) 100 cm (b) 10 cm
−5
(c) 10 cm (d) 10 cm
56. A 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 2𝑚 away.
The distance between the first dark fringe on either side of the central maximum is
(a) 0.6 mm (b) 1.2 mm
(c) 1.8 mm (d) 2.4 mm
57. In a diffraction experiment (of Fraunhoffer type) with a single slit if the wavelength of
the light used is equal to the slit width. Which of the following is TRUE?
(a) diffraction pattern disappears
(b) the central maximum fills the entire screen
(c) theory used becomes invalid
(d) the pattern is unaffected
58. A diffraction grating has 104 lines per inch. It is illuminated at normal incidence by
sodium light (𝜆1 = 5892Å and 𝜆2 = 5896Å). What is the angular separation between
the first-order maxima of these lines?
(a) 1.2 × 0−4 rad
(b) 2.4 × 0−4 rad
(c) 0.6 × 0−4 rad
(d) 1.8 × 0−4 rad
59. Consider a slit of width 18𝜇m which is being illuminated simultaneouslywith light of
orange colour (wavelength 600 nm ) and of blue color (wavelength 450 nm ). The
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diffraction pattern is observed on a screen kept at a distance in front of the slit. The
smallest angle at which only the orange color is observed is 𝜃1 and the smallest angle at
which only the blue color is oserves is 𝜃2 . The angular difference 𝜃2 − 𝜃1 (in degrees)
is___________
60. Consider a point source of light kept at distance outside a transparent, solid cylinder on
its axis and near the end face (base). The minimum refractive index of the material of
the cylinder for which none of the rays entering the base will emerge from the curved
surface is
(a) 2.0 (b) 1.414
(c) 1.515 (d) 1.586
61. The minimum number of lines in plane diffraction grating required to just resolved the
sodium doublet (5890Å and 5896Å) in first order is
(a) 246 (b) 982
(c) 1964 (d) 491
62. A monochromatic plane wave (wavelength = 600 nm) 𝐸0 exp⁡[𝑖(𝑘𝑧 − 𝜔𝑡)] is incident
⃗ 1 ⋅ 𝑟 − 𝜔𝑡)⌋ in the
normally on a diffraction grating giving rise to a plane wave 𝐸1 exp⁡⌊𝑖(𝑘
first order of diffrac-
⃗ 1 | [1 𝑥ˆ + √3 𝑧ˆ].
tion. Here 𝐸1 < 𝐸0 and ⃗k1 = |𝑘 2 2
The period (in 𝜇𝑚 ) of the diffraction grating is (upto one decimal place)
63. The diffiraction pattern from a grating with 𝑁 slits is shown in the figure. The value of
𝑁 is
(a) 3 (b) 5
(c) 4 (d) 2
64. What is the minimum thickness of the base of a prism that can just resolve the two lines
of sodium light centred at 5890Å and 5896Å The given value of refractive index of
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prism material is 1.6545 at wavelength 6563Å and 1.6635 at wavelength 5270Å ?

(a) 8 mm (b) 10 mm
(c) 12 mm (d) 14 mm
65. The radii of the circles of a zone plate by 𝑟𝑛 = 0.1√𝑛 cm. The most intense focal point
for wavelength 𝜆 = 5 × 10−5 cm will be at a distance
(a) 50 cm (b) 100 cm
(c) 150 cm (d) 200 cm
66. Two coherent sources, whose intensity ratio is 25: 16, produce interference fringes. The
ratio of the maximum and minimum intensities of the fringes system will be
(a) 25: 1 (b) 25: 16
(c) 5: 4 (d) 81: 1
67. For the arrangement given in the following figure, the coherent light source 𝐴, 𝐵 and 𝐶
have individual intensities of 2 mW/m2 , 2 mW/m2 and 5 mW/m2 , respectively at point
𝑃. The wavelength of each of the sources is 600 nm. The resultant intensity at point
𝑃( in 𝑚𝑊/𝑚2 ) is
68. A Young's double slit apparatus has a slit separation of 0.5 mm and a screen placed at a
distance of 1000 cm from the slits. When illuminated by a 632 nm Helium-Neon laser,
the position of the first intensity minimum with respect to the central maximum will be
(a) 31.6𝜇m (b) 63.2𝜇m
(c) 316𝜇m (d) 632𝜇m
69. The distance between the successive intensity maxima seen on the screen in a Young's
doubleslit experiment is found to be 𝑠. Suppose now the experiment is repeated with
the spacing between the two slits being doubled and the whole apparatus being
immersed in water ( earlier it was in air ). the fringe spacing will now be ( take the
refractive index of water to be 4/3 )
(a) 𝑠/2 (b) 𝑠
(c) 5𝑠/2 (d) 3𝑠/4
(e) 3𝑠/8
70. Consider two sinusodial waves with same frequency and travelling in the same
direction having
𝜋
a 2 phase difference between them. If the amplitudes of the waves are respectively
6.0 cm and 8.0 cm, the amplitude of the resultant wave is
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(a) 100 cm (b) 14 cm

(c) 5.29 cm (d) 10 cm
71. An anti-reflection film coating of thickness 0.1𝜇m is to be deposited on a glass plate for
normal incidence of light of wavelength 0.5𝜇m. What should be the refractive index of
the film?
(Specify your answer to two digits after the decimal point )
72. A ray of light strikes a glass plate at an angle of incidence 60∘ . If the reflected and
refracted rays are perpendicular to each other, the refractive index of glass is
73. A ray of light is incident on the surface of a glass plate of refractive index 1.5 at the
polarizing angle. The angle of refraction is (degree).
74. If the refractive index for the ordinary ray for calcite and Canada balsam are 1.6584 and
1.5500 respectively, the maximum allowable angle of incidence with the axis of
symmetry of the nicol prism so that ordinary ray is still quenched is
(a) 10∘ (b) 20∘
(c) 30∘ (d) 40∘
75. Two nicols are crossed to each other. Now one of them is rotated through 60∘ . What
percentage of incident unpolarized light will pass through the system?
(a) 25% (b) 27.5%
(c) 35% (d) 37.5%
76. Plane polarized light is incident normally on a plate of doubly refracting uniaxial crystal
with faces cut parallel to the optic axis. The ratio of intensities of 𝐸-and 𝑂-rays if the
light is incident with vibrations making an angle of 30∘ with the face of the crystal is
(Given 𝜆 = 5993Å, 𝜇𝑒 = 1.5532 and 𝜇0 = 1.5442).
1
(a) 1 (b) 3
2
(c) 3 (d) 3
77. The thickness of a quarter-wave plate for light of wavelength 6000 A, the refractive
indices for ordinary and extra-ordinary rays being 1.544 and 1.553 respectively, is__
𝜇m
𝜆
78. The thickness of double refacting crystal to introduce a path difference of 2 between 𝑂-
and 𝐸 rays when 𝜆 = 5893𝐴, 𝜇0 = 1.5442 and 𝜇𝐸 = 1.5533 is
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(a) 323.8 nm (b) 32.38 nm

(c) 212.8 nm (d) 21.28 nm
79. Plane polarized light is incident on a quartz plate cut parallel to the optic axis. The least
thickness of the plate for which the ordinary and extraordinary ray combine to form
plane polarized light on emergence is
(𝜇0 = 1.5442, 𝜇𝐸 = 1.5533, 𝜆 = 5893𝐴)
(a) 23𝜇m (b) 33𝜇m
(c) 43𝜇m (d) 53𝜇m
80. The electric field of two linearly polarized waves are given by
𝐸⃗1 = 𝑖ˆ𝐸𝑥 cos⁡(𝜔𝑡 − 𝜃1 ) and 𝐸⃗2 = 𝑗ˆ𝐸𝑦 cos⁡(𝜔𝑡 − 𝜃2 )
The nature of polarization of the superimposed wave is :
(a) Unpolarized (b) Linearly polarized
(c) Circularly polarized (d) Elliptically polarized
81. An electromagnetic wave is elliptically polarized in the 𝑋 - 𝑌 plane. The direction of the
Poynting vector is in the
(a) 𝑍-direction (b) 𝑋-direction
(c) 𝑌-direction (d) 𝑋𝑌-plane
82. A propagating electromagnetic wave is given by 𝐸⃗ = 𝐸0 (𝑗ˆ + 𝑖𝑘ˆ)𝑒 𝑖(𝑘𝑥−𝜖𝑥) . The wave is
(a) left circularly polarized
(b) right circularly polarized
(c) linearly polarized
(d) elliptically polarized
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Answer Key:
1 D 21 D 41 1.19 61 B 81 A
2 C 22 A 42 D 62 1.2 82 C
3 B 23 C 43 B 63 B 83
4 A,B,C 24 C 44 B 64 D 84
5 D 25 D 45 A 65 D 85
6 C 26 D 46 8 66 D 86
7 C 27 C 47 D 67 5 87
8 9 28 C 48 C 68 D 88
9 1.2 29 A 49 2500 69 E 89
10 B 30 A,D 50 A 70 D 90
11 B 31 A 51 C 71 1.25 91
12 B 32 A 52 D 72 1.732 92
13 C 33 B 53 D 73 33-34 93
14 A 34 C 54 A 74 B 94
15 C 35 C 55 C 75 D 95
16 B 36 C 56 D 76 D 96
17 D 37 E 57 B 77 16-17 97
18 C 38 D 58 C 78 A 98
19 C 39 A 59 0.48 79 B 99
20 D 40 C 60 B 80 D 100
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Quanta Institute LLP

3. A student sets up Young's double slit experiment with electrons of momentum 𝑝

4. (MSQ) A plane polarized electromagnetic wave propagating in 𝑦 − 𝑧 plane is incident at

5. The electric field of an electromagnetic wave is given by 𝐸⃗ = 3sin⁡(𝑘𝑧 − 𝑡)𝑥ˆ + 4cos⁡(𝑘𝑧 −

The emergent electromagnetic wave would be

9. A monochromatic plane wave (wavelength = 600 nm)𝐸0 exp⁡[𝑖(𝑘𝑧 − 𝜔𝑡)] is incident

(a) 2cos⁡𝛿 + 2cos⁡2𝛿

(a) Zero for 𝑛 = 1,2,3 …

(c) 3𝜆/4𝑛 (d) 𝜆/𝑛

25. An electromagnetic wave is incident on a water-air interface. The phase of the

(a) 𝐼0 (b) 0.96𝐼0

As a result, a beam of coherent monochromatic light of wave vector 𝑘 = 2𝜋/𝜆

(a) recording the spectrum in the lowest order

prism material is 1.6545 at wavelength 6563Å and 1.6635 at wavelength 5270Å ?

(a) 100 cm (b) 14 cm

(a) 323.8 nm (b) 32.38 nm

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