Download PHE-09 (2007

PHE-09
Assignment Booklet
Bachelor's Degree Programme
Optics (PHE-09)
(Valid until June 30, 2008)
School of Sciences
Indira Gandhi National Open University
Maidan Garhi, New Delhi
2007-08
Dear Student,
We hope you are familiar with the system of evaluation to be followed for the Bachelor’s Degree
Programme. At this stage, you may probably like to re-read the section on assignments in the Programme
Guide 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 two tutor-marked assignments (TMA) for
this course.
Instructions for Formatting Your Assignments
Before attempting the assignment please read the following instructions carefully.
1) On top of the first page of your TMA answer sheet, please write the details exactly in the following
format:
ENROLMENT NO.:……………………………………………
NAME :……………………………………………
ADDRESS :……………………………………………
……………………………………………
……………………………………………
COURSE CODE:
…………………………….
COURSE TITLE :
…………………………….
ASSIGNMENT NO. ………………………….…
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) While solving problems, clearly indicate the question number along with the part being solved. Be
precise. Write units at each step of your calculations as done in the text because marks will be
deducted for such mistakes. Take care of significant digits in your work. Recheck your work before
submitting it.
6) This assignment will remain valid until June 30, 2008. However, you are advised to submit it
within 8 weeks of receiving this booklet to accomplish its purpose as a teaching-tool.
Answer sheets received after the due date shall not be accepted.
We strongly feel that you should retain a copy of your assignment response to avoid any unforeseen
situation and append, if possible, a photocopy of this booklet with your response.
We wish you good luck.
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Tutor Marked Assignment-1
Optics (PHE-09)
Course Code: PHE-09
Assignment Code: PHE-09/TMA-1/2007-08
Max. Marks: 100
Note: This assignment is based on Blocks 1 and 2. Write answers in your own words.
1. i)
Draw a line diagram showing the directions of oscillations of electric and magnetic field
vectors associated with a plane electromagnetic wave propagating along the positive
x-axis.
(3)
ii)
Draw a ray diagram indicating the propagation of light waves from a medium of
refractive index n1 to a medium of refractive index n2, when (a) n1 < n2, and (b) n1 > n2.
(3)
iii) Why should there be a phase change by  when light strikes the boundary from the side
of a rarer medium?
(3)
iv) The human eye has striking similarity with a camera having automatic focal control.
Explain the automatic focal control functions of the human eye.
(3)
v) Under what condition(s) unpolarised light reflected at the interface separating two media
of different refractive indices become plane polarised.
(3)
vi) Explain the role of convergence in image formation on the retina.
2. i)
(3)
Two plane polarised light waves are propagating along the positive z-direction such that
their electric field vectors are mutually perpendicular. These waves are superposed.
Obtain the condition under which the resultant wave will be circularly polarised.
(6)
ii) Using Fermat’s principle, derive Snell’s law of refraction.
(6)
iii) List the dimensions of colour and the physical parameters associated with them. Discuss
the basis on which Young proposed that there were three types of receptors for colour
vision.
(5)
3. i)
A beam of light is propagating in vacuum and its frequency is constant. Show that the
average energy carried by it per unit area is proportional to the amplitude of the
associated electric field vector.
(5)
ii) Three polarisers are kept on each other in such a way that the transmission axis of each is
turned clockwise by 30 with respect to the transmission axis of the preceding one. If an
unpolarised beam of light is incident on this stack of polarisers, calculate the intensity of
the transmitted beam in terms of the intensity of the incident beam.
(5)
iii) For a crystal, the refractive index no for the o-ray is 1.5442 for light of wavelength
6107 m. The least thickness of the crystal used as a quarter wave plate is found to be
1.65105 m. Determine the refractive index ne for the e-ray in this crystal.
(5)
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In the Young’s double slit experiment, a thin transparent sheet is placed in the path of one
of the interfering beams of light. Will the fringe pattern be affected? Justify your answer.
(3)
ii) Discuss the effect of slit separation on the nature of fringe pattern obtained in Young’s
double slit experiment.
(3)
4. i)
iii) Explain the formation of coherent sources in the biprism experiment to obtain
interference fringe pattern.
(3)
iv) Why is the Fabry-Perot interferometer considered better than the Michelson
interferometer?
(3)
v) Explain why the central spot in Newton’s rings is black? What is the nature of the
interference fringes formed by the air film enclosed between a perfectly plane and a
not-so perfectly plane glass plates?
(3)
vi) In the context of interference of light, differentiate between division of amplitude and
division of wavefront. Give one example each.
(3)
5. i)
What types of interference fringes are produced by thin films? Discuss the conditions for
obtaining them.
(3+4)
ii) With the help of a diagram, explain the working of Michelson interferometer. State the
conditions for obtaining (a) circular, and (b) localised fringes. Explain how Michelson
interferometer can be used for determining the refractive index of a thin plate.
(4+1+1+4)
6. i) The wavelength of light used in Young’s double slit experiment is 6000 Å. The second
and the fourth bright fringes from the centre of the fringe pattern are located respectively
at 10.24 mm and 12.40 mm. If the observation screen is placed at a distance of 1 m from
the slits, calculate the separation between the slits.
(5)
ii) A wedge shaped film is obtained by placing a thin wire between two plane glass plates at
one end keeping them in contact with each other at the other end. When the film is
illuminated by light of wavelength 6000 Å, 40 fringes are observed. Calculate the radius
of the wire.
(5)
iii) Interference fringes are produced by a beam of monochromatic light incident normally on
a wedge shaped film of refractive index 1.5. The angle of the wedge of 15 seconds of an
arc and the two successive dark fringes are 0.4 cm apart. Calculate the wavelength of
light.
(5)
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Tutor Marked Assignment-2
Optics (PHE-09)
Course Code: PHE-09
Assignment Code: PHE-09/TMA-2/2007-08
Max. Marks: 100
Note: This assignment is based on Blocks 3 and 4. Write answers in your own words.
1. i)
Explain the concept of half period elements.
ii) What is the difference between Fresnel and Fraunhofer classes of diffraction?
(3)
(3)
iii) A circular opaque disc of radius r placed at a distance d from a source of monochromatic
light gives rise to diffraction pattern on a screen kept at a distance b from the disc.
Explain why is there a bright spot at the centre of the diffraction pattern.
(3)
iv) Explain the difference between interference and diffraction.
(3)
v) How is the nature of Fresnel diffraction pattern influenced by the change in distance
between aperture / obstacle and the observation screen?
(3)
vi) What do you understand by the resolving power of an optical instrument.
2. i)
(3)
Compare and contrast the qualitative features of diffraction patterns produced by a double
slit and a grating.
(5)
ii) Explain the concept of missing orders in a diffraction pattern.
(5)
iii) Derive an expression for the intensity of the diffraction pattern obtained due to
Fraunhofer diffraction from a single slit.
(7)
3. i)
A grating has 10,000 lines per cm. What is the maximum number of principal maxima
that can be formed for light of wavelength 5105 cm?
(5)
ii) 6 principal maxima are observed in the diffraction pattern due to a diffraction grating.
Calculate the number of lines per cm in the grating if the wavelength of the light is
5000 Å.
(5)
iii) A beam of parallel light of wavelength 6000 Å is incident normally on a 1 rupee coin of
diameter 3 cm. If an observation screen is placed at a distance of 1 m from the coin, how
many Fresnel zones would be obstructed by it (the coin)? For what separation between
the coin and the screen, only 5 zones would be cut off?
(5)
How is the condition for spatial coherence ensured in Young’s double slit experiment?
(3)
ii) List three major differences between an ordinary photograph and a hologram.
(3)
4. i)
iii) What do you understand by acceptance angle of an optical fibre?
(3)
iv) How does a beam of light propagating in an optical fibre restrained from coming out of
the fibre through its cylindrical surface?
(3)
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v) How is the optical communication better than copper cable based communication? (3)
vi) What do you understand by population inversion?
5. i)
(3)
In the context of interference, establish a relation between the visibility of fringes and the
degree of coherence of superposing waves.
(5)
ii) An atomic system consisting of two energy levels with population of higher energy level
less than that of the lower level, is in thermal equilibrium. Show that the absorption of
radiation dominates stimulated emission if radiation of appropriate frequency is
introduced into the system. Comment on the consequences of this fact for laser action.
(7)
iii) Why pumping is necessary for laser action? Compare and contrast three level and four
level pumping schemes for lasers.
(5)
6. i)
Two energy levels of an atomic system are separated by energy corresponding to
frequency 5.01014 Hz. Assume that all atoms are in one or the other of these two energy
levels. Compute the fraction of atoms in the upper energy level at temperature 600 K.
Take kB = 1.38  1023 JK1 and h = 6.6  1034 Js.
(5)
ii) The refractive indices of the core and cladding materials of an optical fibre are 1.64 and
1.53 respectively. Calculate the numerical aperture and light gathering capacity of the
fibre.
(5)
iii) In a laser, the lasing levels are the first and second excited states of the active medium.
The energy value of the first exited state is 1.5 eV and that of the second excited state is
2.2 eV. Calculate the frequency of the laser light.
(5)
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