Assignment Booklet: Waves and Optics

BPHCT-137
ASSIGNMENT BOOKLET
BACHELOR’S DEGREE PROGRAMME

(B.SC.G)
WAVES AND OPTICS
Valid from 1st January, 2022 to 31st December, 2022
School of Sciences
Indira Gandhi National Open University
Maidan Garhi, New Delhi-110068
(2022)
Dear Student,
Please read the section on assignments in the Programme Guide for B. Sc. that we sent you
after your enrolment. A weightage of 30 per cent, as you are aware, has been earmarked for
continuous evaluation, which would consist of one tutor-marked assignment for this course.
The assignment is in this booklet, and it consists of two parts, Part A and B. The total marks of
all the parts are 100, of which 35% are needed to pass it.
Instructions for Formatting Your Assignments
Before attempting the assignment please read the following instructions carefully:
1) On top of the first page of your answer sheet, please write the details exactly in the following
format:
ROLL NO.: ….…………………………………………

NAME: …………………………………………………
ADDRESS: ……………………………………………
………………………………………………………….
………………………………………………………….
COURSE CODE:………………………….
COURSE TITLE: …………………………
ASSIGNMENT CODE: …………………..
STUDY CENTRE: ……………………….. DATE: …………………….………………...
PLEASE FOLLOW THE ABOVE FORMAT STRICTLY TO FACILITATE EVALUATION

AND TO AVOID DELAY.
2) Use only foolscap size writing paper (but not of very thin variety) for writing your answers.
3) Leave 4 cm margin on the left, top and bottom of your answer sheet.
4) Your answers should be precise.
5) Solve Part A and Part B of this assignment, and submit the complete assignment answer
sheets containing Parts A and B within the due date.
6) The assignment answer sheets are to be submitted to your Study Centre as per the
schedule. Answer sheets received after the due date shall not be accepted.
We strongly suggest that you retain a copy of your answer sheets.
7) This assignment is valid from 1st January, 2022 to 31st December, 2022. If you have failed
in this assignment or fail to submit it by 31st December, 2022, then you need to get the
assignment for the year 2023, and submit it as per the instructions given in the Programme
Guide.
8) You cannot fill the examination form for this course until you have submitted this
assignment. For any queries, please contact: srjha@ignou.ac.in, drsgupta@ignou.ac.in. We
wish you good luck.
2
Tutor Marked Assignment
WAVES AND OPTICS
Course Code: BPHCT-137
Assignment Code: BPHCT-137/TMA/2022
Max. Marks: 100
Note: Attempt all questions. The marks for each question are indicated against it.
PART A
1. a) The mathematical expression for one dimensional wave travelling along the
positive x-direction is given as
y ( x, t )  0.02 sin (42 x  1886t ) m
where x is in meters and t is in seconds. Determine the direction of propagation of

the wave and calculate its amplitude, wavelength, frequency and velocity. (25)
b) Determine the frequencies of the fundamental mode and the next two harmonics
that can be set up on a sitar string of length 1.0 m. Take the speed of waves of the
string to be 2.8  10 3 ms 1. (5)
c) The electric field vectors of two light waves propagating along the positive z-
direction are given as

E1( z,t )  xˆ E01cos(kz  t )

E 2 ( z,t )  yˆ E02cos(kz  t  )
where x̂ and ŷ are unit vectors along x and y-axes, respectively. Show that when
these two waves superpose, we obtain elliptically polarised light. Also show that
the linear and circular polarisations are special cases of elliptical polarisation. (5+5)
2. a) Derive an expression for the displacement of the nth bright fringe in Young’s
double-slit experiment when a thin transparent plate of refractive index  and
thickness t is introduced in the path of one of the constituent interfering beams of
light. Will there be any change in the fringe-width after the introduction of the
plate? (8+2)
b) i) Distinguish between fringes of equal inclination and fringes of equal thickness. (5)
ii) Newton’s rings are formed in reflected light of wavelength 5890  10 8 cm with a
liquid between the plane and curved surfaces. The diameter of the fifth ring is
0.3 cm and the radius of curvature of the curved surface is 100 cm. Calculate
the refractive index of the liquid, when the ring is bright. (5)
c) Explain how Michelson interferometer is used to determine the refractive index of a
thin plate. (5)
PART B
3. a) What is a zone plate? How does a positive zone plate differ from a negative zone
plate? Show that each Fresnel zone has nearly the same area. (3+3+4)
3
b) In the Fraunhofer diffraction pattern due to a single slit, the intensity of the central
spot is maximum. Explain on the basis of geometrical considerations. (5)
c) The Fraunhofer diffraction pattern due to a single slit of width 0.4 cm is obtained
with the help of a lens of focal length 30 cm. If the wavelength of light used is
5890 Å, calculate the distance of the first dark fringe and the consecutive bright
fringe from the axis. (5)
d) The radius of the fifth zone of a zone plate is 2 mm. Considering the zone plate as
a converging lens, calculate its focal length for light of wavelength 4800 Å. (5)
4. a) What do you understand by spatial and temporal coherence? (3)

b) Explain the meaning of coherence length. (3)
c) What is the difference between spontaneous emission of radiation and stimulated
emission of radiation? (3)
d) How is holography different from ordinary photography? (3)
e) What are the advantages of using optical fibre as communication medium? (3)
5. a) In a laser, the lasing levels are the first excited state and the ground state of the
active medium. If the energy of the first excited state is 1.5eV, calculate the
frequency of the laser light. (5)
b) The refractive index of the core and cladding materials of an optical fibre is 1.46
and 1.38, respectively. Calculate the critical angle, numerical aperture and
acceptance angle at the air-fibre interface. (5)
*******

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BPHCT-137

BACHELOR’S DEGREE PROGRAMME

WAVES AND OPTICS

Valid from 1st January, 2022 to 31st December, 2022

ROLL NO.: ….…………………………………………

PLEASE FOLLOW THE ABOVE FORMAT STRICTLY TO FACILITATE EVALUATION

where x is in meters and t is in seconds. Determine the direction of propagation of

4. a) What do you understand by spatial and temporal coherence? (3)

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