BPHCT-137 (WAVES AND OPTICS)

(Valid from 1st January, 2023 to 31 st December, 2023)

PART A

1. a) The resultant wave due to superposition of two waves of the same frequency, velocity and amplitude travelling in opposite directions on a string fixed at both ends is given as
\[
y(x, t)=2 \sin \frac{\pi x}{6} \cos 20 \pi t \mathrm{~cm}
\]
Determine the equations representing the superposing waves and calculate the distance between two consecutive antinodes.

b) In a fluid medium, the speed of sound waves is \(280 \mathrm{~ms}^{-1}\) and its frequency is 450 \(\mathrm{Hz}\). Calculate the phase difference between two displacements of a particle of the medium at a point at time \(10^{-3} \mathrm{~s}\) apart.

c) Show that when two in-phase linearly polarised light waves are superposed, the resultant wave has fixed orientation as well as amplitude. Depict the orientation of electric field vector of the resultant wave in the reference plane.

2. a) Discuss the principle of Michelson interferometer. How is it used to determine the refractive index of a thin plate?
b) Describe the experimental set up for observing Newton’s rings. 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.

c) The inclined faces of a glass biprism ( \(\mu=1.5)\) make an angle of \(1^{\circ}\) with its base. The biprism is illuminated by a sodium lamp \((\lambda=589 \mathrm{~nm})\) and the eye piece is at a distance of \(1 \mathrm{~m}\) 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 \(0.4 \mathrm{~cm}\) apart in one case and \(0.16 \mathrm{~cm}\) apart in the second case, calculate the width of interference fringes observed on the screen.

PART B
3. a) A vertical single and double slits are 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.

b) Calculate the maximum number of principal maxima that can be formed with a grating having 4500 lines per \(\mathrm{cm}\) for light of wavelength \(490 \mathrm{~nm}\).

4. a) Discuss applications of lasers in medicine and communication.

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 labelled diagram, discuss lasing action of a He-Ne laser.

d) List and explain various types of losses in an optical fibre.