UPSC Physics Optional PYQs (CSE & IFoS)PYQs

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.

Discuss the properties of Cornu spiral. Show that the spiral can be used to obtain the intensity distribution in the Fresnel's diffraction pattern due to a straight edge.

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

(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.

(i) What is Holography ? (ii) Show with simple diagrams, how a hologram is written and read using a laser. (iii) Mention some important applications of holography.

(i) Using the concept of spontaneous and stimulated emission of radiation, obtain the relation between Einstein's A and B coefficients. (ii) What is the physical significance of Einstein's A coefficient ? (iii) Justify why lasing action is much more difficult at X-ray frequency than in case of infrared frequency spectrum.

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

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.

(i) In a Michelson's interferometer, 100 fringes cross the field of view when the movable mirror is displaced through 2\cdot 894 \times 10^{-3}~\text{cm}. Calculate the wavelength of the monochromatic source of light. (ii) A shift of 200 fringes is observed when the movable mirror of a Fabry-Pérot interferometer is shifted by 0\cdot 0298~\text{mm}. Calculate the wavelength of the incident radiation.

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.

Explain the principle of (i) induced absorption, (ii) spontaneous emission and (iii) stimulated emission. Show that the ratio of Einstein's coefficients is given by \frac{A}{B}=\frac{8\pi h\nu^{3}}{c^{3}}

Explain the principle of producing polarized light by the method of reflection, refraction and double refraction with the help of neat diagrams.

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

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.

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 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?

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.

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