UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Monochromatic light of wavelength due to diffraction, and critically; comment on [Source text is incomplete in the available scan.]

Derive an expression for the resolving power of a diffraction grating.

Plane waves pass through a slit whose plane is parallel to the wave fronts. Obtain an expression for the angular spread of the central maximum due to diffraction, and critically comment on the result.

How can one produce (i) left-handed circular motion, and (ii) right-handed circular motion by combining two simple harmonic motions? Justify, your answers.

Parallel light is incident normally on diffraction grating having 6,000 lines per cm. Find the angular separation between the maxima for wavelengths 5,890 Å and 5,896 Å in the second order.

Out of the following three functions only one can be Fourier analysed in the range -\pi \leqslant x \leqslant \pi. Choose the correct function and obtain its Fourier series expansion: (i) f(x) = x^{2} \text{ for } 0 < x < \pi (ii) f(x) = 0 \text{ for } -\pi < x < 0 = \pi \text{ for } 0 < x < \pi (iii) f(x) = 1/x^{2} \text{ for } -\pi < x < \pi

Using Huyghens' construction, discuss the propagation of O and E waves in a biaxial crystal when the optic axis is perpendicular to the plane of incidence and parallel to the boundary surface. Take the incident ray to be oblique.

Define and explain the terms resolving power and magnifying power of an optical instrument. For a telescope, on that parameter do these depend? For a given resolving power, what is the optimum magnifying power?

What is stimulated emission of light? How does it differ from spontaneous emission? Name any device basal on the stimulated emission of light and explain its working.

Write a note on Uses of multiple beam interferometry.

The angular frequency, \omega, of a wave is related to the wave vector, k, by the relation \omega = \omega_{0} \sin\frac{ka}{2} \text{ for } 0 < k > \frac{\pi}{a} Determine the phase and group velocities of this wave and draw a rough sketch to show their variation with k(0 < k < \pi/a)