Search, filter, and study UPSC Civil Services & IFoS Physics past year questions with rigorous derivations, formulas, and step-by-step solutions.
Discuss briefly the features of 'guard rings'. The plates of a capacitor are square-shaped, each of side l. The plates are inclined at an angle \alpha to each other. The smallest distance between the plates is a. Calculate the capacitance when \alpha is small.
Why does a soap bubble expand upon electrification? A sphere of radius R contains a charge +Q and a charge -Q distributed uniformly in the upper and lower hemispheres respectively. Show that the dipole moment of charge distribution is \dfrac{3}{4}QR\hat{k}, where \hat{k} is directed along the polar axis of the spherical coordinate system.
A current i(t)=(2e^{-t}-e^{-2t})\,\mu\mathrm{A} charges up a 120\,\mathrm{nF} capacitor for a period of 2 seconds. If the final voltage across the capacitor is 15\,\mathrm{V}, what was the initial voltage across it?
A charge q=2\,\mu\mathrm{C} is placed at a=10\,\mathrm{cm} from an infinite grounded conducting plane sheet. Find the (i) total charge induced on the sheet, (ii) force on the charge q and (iii) total work required to remove the charge slowly to an infinite distance from the plane.
Discuss the principle of 'artificial dielectric'. Where do you find its use?
(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.
(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.
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.
Explain the principle of operation of optical fibre. What are the different losses that take place in optical fibre?
How is laser light different from ordinary light? Discuss the working principle of ruby laser. What role do chromium ions play in this process?
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.
Sunlight is reflected from a calm lake. The reflected light is 100% polarized at a certain instant. What is the angle between the sun and horizon?
Discuss absorption loss in an optical fibre comparing and contrasting the intrinsic and extrinsic absorption mechanisms.
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.
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.
Show that the areas of all the half-period zones are nearly the same. Find the radius of 1st half-period zone in a zone plate whose focal length is 50\ \mathrm{cm} and the wavelength of the incident light is 500\ \mathrm{nm}.
(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.
What is multiple-beam interference? Discuss the advantages of multiple-beam interferometry over two-beam interferometry. Explain the fringes formed by Fabry-Perot interferometer.
Explain with proper example the interferences due to 'division of wavefront' and 'division of amplitude'.