UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Calculate the skin depth for radio waves in free space of wavelength 3 m in copper, given that electrical conductivity for copper is 6\times10^{7}\,\Omega^{-1}\,\mathrm{m}^{-1}.

Discuss the growth of current when an e.m.f. is suddenly applied to a circuit containing resistance, inductance and capacitance in series. What is the time constant of the circuit?

A series circuit has an inductance of 200 microhenries, a capacitance of 0.0005 microfarad and a resistance of 10 ohms. Find the resonant frequency and quality factor of the circuit.

What happens if the primary winding of a transformer is connected to a battery?

The electric field for a uniform plane wave in free space is given by \vec{E} = (\hat{x} + \hat{y})10 e^{j 10 z}. Determine the corresponding magnetic field vector.

For two isotropic media with \mu_1 \neq \mu_2 and \varepsilon_1 \neq \varepsilon_2, find an expression for the Brewster angle \theta_b for parallel polarization.

Consider a perfectly conducting half-space as shown below :

A uniform plane wave given by

\begin{align*} \vec{E}^i &= \hat{x} E_0 e^{-j k z} \\ \vec{H}^i &= \hat{y} \frac{E_0}{\eta_0} e^{-j k z} \quad \eta_0 = 120\pi\text{ ohm} \end{align*}

is incident normally on the boundary. Write down the expressions for the reflected electric and magnetic fields.

Two thin symmetrical lenses of two different natures (convex and concave) and of different materials have equal radii of curvature R=15\,\mathrm{cm}. The lenses are put close together and immersed in water \mu_w=4/3. The focal length of the system in water is 30\,\mathrm{cm}. Show that the difference between the refractive indices of two lenses is 1/3.

A laser beam of 1 micrometer wavelength with 3 megawatts power of beam diameter 10\ \mathrm{mm} is focussed by a lens of focal length 50\ \mathrm{mm}. Evaluate the electric field associated with the light beam at the focal point. (Dielectric permittivity of free space, \varepsilon_0=8\cdot8542\times10^{-12}\ \mathrm{C^2/N-m^2})

What should be the refractive index of cladding of an optical fibre with numerical aperture 0.5 with refractive index of core as 1.5?

An unpolarized light beam of intensity 1000\ \mathrm{W/m^2} is incident on an ideal linear polarizer with its transmission axis parallel to vertical direction. Describe an experiment to reduce the intensity of light beam to 500\ \mathrm{W/m^2}.

Obtain the expression for the primary focal length of Fresnel zone plate.

Show that two light beams polarized in perpendicular directions will not interfere.

Describe Michelson interferometer for evaluation of coherence length of an optical beam. Calculate coherence length of a light beam of wavelength 600\,\mathrm{nm} with spectral width of 0.01\,\mathrm{nm}.

An optical beam of spectral width 7.5\,\mathrm{GHz} at wavelength \lambda = 600\,\mathrm{nm} is incident normally on Fabry-Perot etalon of thickness 100\,\mathrm{mm}. Taking refractive index unity, find the number of axial modes which can be supported by the etalon.

(ii) Determine its quality factor Q and width of resonance \Delta f.

Consider a system of two thin lenses of focal lengths +15\text{ cm} and -20\text{ cm} separated by a distance of 25\text{ cm} in air. Determine the system matrix. For an object of height 1\text{ cm} placed at a distance of 27\cdot 5\text{ cm} in front of the convex lens, find the size and position of the image.

A slit 0\cdot 25\text{ mm} wide is placed in front of a convex lens and illuminated by plane waves of wavelength 500\text{ nm}. The Fraunhofer diffraction pattern is formed in the focal plane of the lens. In the pattern, the distance from the third minimum on the left to the third minimum on the right is found to be 3\text{ mm}. Find the focal length of the lens.

(i) Between multimode and single-mode fibers, explain critically how and why single-mode fiber is chosen for communication.

(ii) Why are the two wavelengths 1\cdot 30\ \mu\text{m} and 1\cdot 55\ \mu\text{m} important in single-mode fiber-optical communication system?