PYQ Bank

How is laser light different from ordinary light? Discuss the working principle of ruby laser. What role do chromium ions play in this process?

Discuss absorption loss in an optical fibre comparing and contrasting the intrinsic and extrinsic absorption mechanisms.

A plane-polarized light passes through a double-refracting crystal of thickness 40\,\mu\mathrm{m} and emerges out as circularly polarized. If the birefringence of the crystal is 0.00004, then find the wavelength of the incident light.

State and explain Fermat's principle of extremum path and use the same to deduce the laws of reflection and refraction of light.

Obtain the system matrix for a thin lens placed in air and made of material of refractive index 1.5 having radius of curvature 50\,\mathrm{cm} each. Also find its focal length.

(i) Explain the reason for pulse broadening due to intermodal and material dispersion. Deduce the relation of pulse broadening for intermodal dispersion in optical fiber. (ii) A step index fiber in air has a numerical aperture of 0\cdot 16, a core refractive index of 1\cdot 45 and a core diameter of 60~\mu\text{m}. Determine the normalized frequency for the fiber when light at a wavelength of 0\cdot 8~\mu\text{m} is transmitted. Also estimate the number of guided modes propagating in the fiber.

Explain the principle of operation of optical fibre. What are the different losses that take place in optical fibre?

Find the velocity of sound in a gas in which two waves of wavelengths 1.00\,\mathrm{m} and 1.01\,\mathrm{m} produce 10 beats in 3 seconds.

Although the principle of operation of a basic LASER is based upon two energy levels, why does one need a 3-level or a 4-level scheme to achieve satisfactory lasing ? Explain your answer with special reference to a Ruby-laser.

A diffraction grating has 5000\text{ lines per cm}. For illumination at normal incidence, determine the dispersive power of the grating in the second order spectrum in the range of wavelengths around 500\text{ n.m.}

Discuss the principles of Fresnel's half period zone and explain how these are used in the construction of a zone plate. Show how the zone plate has several foci.

Can D_1 and D_2 lines of sodium light (\lambda_{D_1}=5890\mathring{\mathrm{A}}\ \text{and}\ \lambda_{D_2}=5896\mathring{\mathrm{A}}) be resolved in second-order spectrum if the number of lines in the given grating is 450? Explain.

The refractive indices of core and cladding in a step index optical fiber are 1.52 and 1.48 respectively. The diameter of the core is 30\,\mu\mathrm{m}. If the operating wavelength is 1.3\,\mu\mathrm{m}, calculate the V parameter and the maximum number of modes supported by the fiber.

In Michelson interferometer, 100 fringes cross the field of view when the movable mirror is displaced through 0.029\,\text{mm}. Calculate the wavelength of the light source used.

Obtain the conditions for constructive interference and destructive interference in a thin film due to reflected light.

The vibrations of a string fixed at both ends is represented by the equation y = 2\sin\frac{\pi x}{3}\cos 50\pi t\ (m) If the above stationary wave is produced due to the superposition of two component waves of the same frequency, velocity and amplitude travelling in opposite directions, find (i) the exact equations of the displacements associated with the vibrations of the component waves and (ii) the distance between two consecutive nodes of the stationary wave.

State Huygen's principle. Using this principle and suitable diagram, show that this principle could lead to Snell's law of refraction.

Prove that the group velocity V_g of electromagnetic waves in a dispersive medium is given by V_g = \frac{c}{n + \omega\ dn/d\omega} where c is the velocity of light in vacuum and n is the refractive index of the medium for the angular frequency \omega of the waves.

Obtain an expression for the resolving power of a grating explaining the Rayleigh's criterion of resolution.

The equation of a progressive wave moving on a string is y = 5\sin \pi(0.01x - 2t). In this equation, y and x are in centimetres and t is in seconds. Calculate amplitude, frequency and velocity of the wave. If two particles at any instant are situated 200\,\mathrm{cm} apart, what will be the phase difference between these particles?