UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Thin transparent films produce colours when a white light falls on them or they act as antireflecting coatings. Find the conditions for these characteristics.

(i) When a monochromatic light passes through a single slit, dark and bright fringes are observed on a screen kept far away from the slit. Draw an amplitude and intensity pattern of the light on the screen.

(ii) Write an expression for intensity distribution and give the conditions for bright and dark fringes.

(iii) If the slit width is 0\cdot 3\text{ mm} and the distance between the screen and the slit is about 30\text{ cm}, then what is the angle of diffraction for the first minimum? (\lambda = 5 \times 10^{-5}\text{ cm})

(i) Give the equation of motions for a particle executing simple harmonic motion for undamped, damped and forced vibrations, and explain the terms.

(ii) Give a plot between the displacement and time for each case of the above and interpret.

(iii) What are the conditions for critical damping and resonance?

A plane transmission grating has 3000 lines in all, having width of 3\ \mathrm{mm}. What would be the angular separation in the first order spectrum of the two sodium lines of wavelengths 5890\mathring{\mathrm{A}} and 5896\mathring{\mathrm{A}}? Can they be seen distinctly?

Calculate the focal lengths of the components of an achromatic telescope objective having a power of +3\cdot 333 diopter, made from crown glass and flint glass, whose dispersive powers are 0\cdot 012 and 0\cdot 02 respectively.

Distinguish between positive and negative crystals in terms of double refraction. How are these crystals used to make quarter wave plates? Explain how the quarter wave plate is used in producing elliptically and circularly polarized light.

Discuss the intensity distribution in Fraunhofer diffraction pattern due to a single slit. Obtain conditions for maxima and minima of the intensity distribution. Show that the intensity of the first maxima is about 4.95\% of that of the principal maxima.

When the two waves of nearly equal frequencies interfere, then show that the number of beats produced per second is equal to the difference of their frequencies.

With the help of a neat diagram, explain spherical aberration. Briefly discuss the methods to minimize spherical aberration.

Explain the principle and working of He-Ne laser. What is the role of He gas? Why is it necessary to use narrow tube? How many longitudinal modes can be excited for an He-Ne laser in a cavity of length 30 cm and having half width of gain profile of laser material 2 \times 10^{-3}\,\mathrm{nm}? The emission wavelength is 6328\,\mathring{\mathrm{A}}.

What do you mean by spherical aberration of a lens? Show that if two plano-convex lenses are kept at a distance equal to the difference of their focal lengths, the spherical aberration would be minimum.

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.

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.

Explain with proper example the interferences due to 'division of wavefront' and 'division of amplitude'.

What is multiple-beam interference? Discuss the advantages of multiple-beam interferometry over two-beam interferometry. Explain the fringes formed by Fabry-Perot interferometer.

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) 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.

A parallel beam of light of wavelength 5890~\text{\AA} is incident at an angle of 30^\circ on a plane transmission grating with 15000 lines/inch. Find the highest order of spectrum that can be observed.

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.