UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Explain in detail how one can obtain fringes with the Michelson Interferometer using incandescent lamps.

A book sits on a horizontal board that is undergoing simple harmonic motion with amplitude of 1\text{ m}. The coefficient of friction between the book and the board is \mu = 0.5. Find the frequency of the motion of the board at which the book is about to slip.

The case of a Simple Harmonic Progressive Wave traversing through a medium is expressed as y = 4 \times 10^{-5} \sin(600\ \pi t + \varphi) Determine

(i) amplitude of vibration of the particles.

(ii) wavelength of the sound wave and

(iii) the phase difference between the particles situated at a distance of 22\text{ cm}. (The sound velocity in the medium is 3.4 \times 10^4\text{ cm/s}).

The maximum pressure variation P that the human ear can tolerate in loud sounds is about 28\text{ nt/m}^2. Normal atmospheric pressure is about 100,000\text{ nt/m}^2. Find the corresponding maximum displacement for a soundwave in air having a frequency of 100\text{ cycles/second}. (Take velocity of sound in air as 331\text{ m/sec.} arid density of air = 1.22\text{ kg/m}^3)

When fixed at both ends, a wire under tension of 900\text{ N} and having a linear density 10^{-2}\text{ kg/m} is resonant at the frequency of 420\text{ Hz}. The next higher frequency at which it resonates is 490\text{ Hz}. What is the length of the wire.

Write a short note on Holography.

Sodium light is incident normally upon a plane transmission grating having 5000 lines/cm. Calculate the angular separation of the D_1 and D_2 lines in the first order spectrum. As this angular separation is very sexy small, how can one magnify it 10 times ? (Given : \lambda_{v1} = 5690\text{ \AA} and \lambda_{v2} = 5896\text{ \AA})

Differentiate between Fresnel and Fraunhoffer diffractions. How can one explain the Fresnel diffraction pattern due to a straight edge?

Give Rayleigh's criterion for resolution. Why telescopes with larger objectives are better? The objective of the telescope at St. Palomer has a diameter of 5.08 m. What is the least distance on Moon which could be resolved by it? (Given distance of moon from the Earth = 3,84,000 km and \lambda = 5890\text{ \AA}).

Why an extended source is necessary to see colours in a soap-film ? Non-reflecting surfaces are made by coating very thin films of a transparent material. Find the maximum thickness of such thin coatings given that \lambda = 5.5 \times 10^{-5}\text{ cm} and \mu = 5/4.

Write a short note on Holography.

What are the essential conditions for observing the interference of light? Two coherent sources with intensity ratio 4 : 1 interfere. Find I_{\text{max}} / I_{\text{min}}.

Calculate the peak values of \vec{E} and \vec{B} for a laser beam of power 2 \times 10^{10}\text{ W} and radius 0.1 mm.

A short-focus lens is used to focus a laser beam of wavelength 6328 Å. If the beam width is comparable to the focal length of the lens, calculate the area of cross-section of the region of focus.

The equation of a one-dimensional propagating harmonic transverse wave is given by: y = 8 \sin 30\pi \left(t - \frac{x}{240}\right) \text{meter} Find the resultant wave formed by the superposition of the incident and the reflected waves from a rigid end. Also determine the amplitude of stationary waves formed at x = 2\text{ meter}. What will be the distance between consecutive nodes ?

Write a short note on Forced oscillations.

What are damped oscillations ? Obtain the differential equation for damped oscillations and write its possible solution. Explain with corresponding sketches, when there can be very heavy damping, critical damping and weak damping.

Explain why a two-level system is not adequate for laser operation. Draw the essential parts of a ruby laser and explain the working principle with the help of an energy level diagram.

Distinguish between spatial and temporal coherence of light. What kind of coherence is required for interference and diffraction? Explain why it is possible to produce interference effects using two tuning forks of the same frequency but not by two independent sources of light of the same wavelength.

Consider a resonant cavity of volume V of a container to which a neck of area of cross section a and length l is attached. Show that the product of the square of resonance frequency n and volume V is constant. Comment on the correction needed to the derived relation between n^2 and V. How will you determine this correction?