Calculate the path difference between interference rays in reflected light from a thin film of thickness t and refractive index M.

The electric field vectors of two linearly polarised light waves are given by

E1 ex E01 cos (kz

and E2 ey E02 cos (kz

Show that their superposition leads to an elliptically polarised light wave.

Calculate the numerical aperture for a fibre having core and cladding with refractive indices 1·5 and 1·45, respectively. Draw the refractive index profile of a gradient index

Show that a zone plate acts like a multi-foci converging lens.

State Fermat's principle and use it to derive the laws of refraction.

The rate of energy radiated by the Sun is 4·0 x 10^26 Js^-1. Calculate the Poynting vector at the surface of the Earth. Take the radius of the Sun as 7 x 10^8.m and the distance between the Sun and the Earth as 1·5 x 10^11 m.

3. Derive an expression for the intensity of transmitted light in a Fabry -Perot interferometer. Discuss the sharpness of fringes. How is Fabry -Perot interferometer superior to Michelson interferometer?

Newton's rings are produced in reflected light of wavelength 600 nm with a liquid between the plane and curved surfaces. The diameter of the fifth bright ring is 0·3 cm and the radius of curvature of the curved surface is 110 cm. Calculate the refractive index of the liquid.

Circular fringes are observed in a Michelson interferometer illuminated by light of wavelength 600 nm. When the path difference between the mirrors M1 and M2 is 0·25 cm, the central fringe IS bright. Calculate the angular diameter of the sixth bright fringe.

Discuss transition from Fresnel diffraction pattern to Fraunhofer diffraction pattern.

A slit of width b is illuminated by light of wavelength A. The intensity of the diffraction pattern at an angle e with the horizontal axis is given by

I8 Io(sin where B nb sin8/A

Determine the positions of secondary maxima and show that the intensity of the first secondary maximum is only 4·96% of the central maximum.

With the help of appropriate diagrams, discuss Rayleigh criterion for resolving nearby images.

What do you understand by resolving power of a microscope Establish the relation between resolving power and numerical aperture fora microscope.

For two curves having equal intensity, show that the resultant of the curves will dip by nearly 20% according to Rayleigh criterion.

Derive expressions for Einstein's A and B coefficients.

Explain the process of image reconstruction in a hologram.

What is a step-index fibre Obtain an expression for the angle of incidence beyond which light will get refracted into the cladding material. What will happen if the refractive index of the cladding is higher than that of the core?