BPHCT-137 EM 2025 SOLVED ASSIGNMENT

Description

Tutor Marked Assignment
WAVES AND OPTICS
Course Code: BPHCT-137
Assignment Code: BPHCT-137/TMA/2025
Max. Marks: 100
Note: Attempt all questions. The marks for each question are indicated against it.
PART A
1. a) A sinusoidal wave is described by
y (x, t) = 3.0 sin (3.52t − 2.01x) cm
where x is the position along the wave propagation. Determine the amplitude,
wave number, wavelength, frequency and velocity of the wave.
b) A stretched string of mass 20 g vibrates with a frequency of 30 Hz in its
fundamental mode and the supports are 40 cm apart. The amplitude of vibrations
at the antinode is 4 cm. Calculate the velocity of propagation of the wave on the
string.
c) Show that superposition of two linearly polarised light waves having different
amplitudes and a finite phase difference can be used to produce elliptically plane
polarised waves. Also show that the linear polarisation and circular polarisation are
special cases of elliptical polarisation.
2. a) What is a biprism? The inclined faces of a glass biprism ( = 1.5) make an angle of
1 with its base. The biprism is illuminated by sodium lamp ( = 589 nm) and the
eye piece is at a distance of 1 m from the slit. A convex lens inserted between the
biprism and the eye piece gives clear images of coherent sources in the focal
plane of the eye piece. If the images are 0.4 cm apart in one case and 0.16 cm
apart in the second case, calculate the width of interference fringes observed on
the screen.
b) i) Show that the radius of a dark Newton’s ring is directly proportional to the
square root of the radius of curvature of the lens used.
ii) Newton’s rings are formed in reflected light of wavelength
5890
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.
(25)
(5)
(5+5)
(2+8)
(5)

10

8
cm
with a
(5)
c) Explain how Michelson interferometer is used to determine the wavelength of light. (5)
PART B
3. a) A vertical single and double slits and illuminated by a point source. Discuss the
salient features of their Fraunhofer diffraction patterns. Also, obtain an expression
for intensity distribution in case of double slit.
(5+5+10)
b) ‘Diffraction limits the image forming capability of optical devices’. Discuss the
authenticity of this statement for the particular case of a microscope.
(5)
3
4. a) Discuss applications of lasers in medicine and communication.
(5)
b) Define numerical aperture and angle of acceptance. An optical fiber has a
numerical aperture of 0.20 and cladding refractive index of 1.59. Calculate the
refractive index of the core material and the acceptance angle of the fibre in
water whose refractive index is 1.33.
c) With the help of a labeled diagram, discuss lasing action of a He-Ne laser.
d) The refractive index of the core and cladding materials of an optical fibre is 1.52
and 1.46, respectively. Calculate the critical angle, numerical aperture and
acceptance angle at the air-fibre interface.