Question 1. a) The sodium lamp used in a physics laboratory gives out light uniformly. Suppose that the lamp uses 40 W. Calculate the magnitude of electric field.

b) Describe polarisation of light by reflection. How does degree of polarisation vary with angle of incidence of light?

c) Discuss the concept of missing orders with reference to double slit diffraction pattern.

d) Depict spatial evolution of Fresnel diffraction pattern.

Question 2. a) Obtain expressions for reflection and transmission amplitude coefficients when electric vector associated with a plane monochromatic electromagnetic wave is in the plane of incidence.

b) Obtain an expression for elliptically polarised light resulting due to superposition of two orthogonal linearly polarised light waves. Show that plane polarised light and circularly polarised light are special cases of elliptically polarised light.

Question 3. a) Obtain the expression for shift in fringes when a thin transparent sheet is introduced in the path of one of the waves in a double slit interference experiment.

b) A plano-convex lens of radius 1.0 m is placed on an optically flat glass plate and is illuminated by an extended monochromatic source. Assume that the point of contact is perfect. The diameters of the 10th and 5th dark rings in the reflected light are 4.50 × 10^-3m and 3.36 × 10^-3m. Next, the space between the lens and the glass plate 3 is filled with a liquid. The diameter of the 5th ring changes to 3.0×10 m.

Calculate the refractive index of the liquid when the ring is (i) dark, and (ii) bright, if the wavelength of light is 589 nm.

Question 4. a) A plane light wave of wavelength 580 nm falls on a long narrow slit of width 0.5 mm.

(i) Calculate the angles of diffraction for the first two minima. (ii) How are these angles influenced if the width of slit is changed to 0.2 mm?

(iii) If a convex lens of focal length 0.15 m is now placed after the slit, calculate the separation between the second minima on either side of the central maximum.

b) Discuss Rayleigh's criterion for resolving power of an optical instrument. Obtain an expression for resolving power of a microscope.

Question 5. a) 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.

b) Two energy levels of an atomic system are separated by energy corresponding to frequency 3.0 × 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 400 K. Take k_B = 1.38×10-²³J -1 and h = 6.6×10^-34Js.

c) The refractive indices of the core and cladding materials of an optical fibre are 1.51 and 1.39 respectively. Calculate the numerical aperture and light gathering capacity of the fibre.