PYQ Bank

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.

The electromagnetic field inside a device is given by \vec{E} = \hat{y} E_0 \sin(k_x x) e^{-j k_z z}, \quad\text{where } k_x = \frac{n\pi}{a} \vec{H} = E_0 [\hat{x} \frac{-k_z}{\omega\mu} \sin(k_x x) + \hat{z} \frac{j k_x}{\omega\mu} \cos(k_x x)] e^{-j k_z z} Obtain an expression for the z-component of time-averaged Poynting vector \vec{S}.

Show that when the temperature T of a radiating object is not too different from the surrounding temperature T_0, the object obeys Newton's law of cooling.

If the magnetic moment of proton is 2.793\ \mu_N calculate, giving necessary steps, the radio frequency at which nuclear magnetic resonance occurs in water kept in a uniform magnetic field of 2.4\text{ T}.

A radiation gas of temperature T fills a cavity of volume V. The system expands adiabatically and reversibly to a volume equal to 8V. By what factor does the temperature change?

The following inputs are given :

\begin{align*} T_0 &= 5500\text{ K} && \text{(Sun surface temperature)}, \\ R &= 7 \times 10^{10}\text{ cm} && \text{(Sun radius)}, \\ r &= 6\cdot 4 \times 10^8\text{ cm} && \text{(Earth radius)}, \\ D &= 1\cdot 5 \times 10^{13}\text{ cm} && \text{(Sun--Earth distance)}. \end{align*}

Assume that the earth and the sun both absorb all electromagnetic radiations incident on them, and that the earth is at a constant temperature T over the day-night cycle. Calculate T.

A long wire of radius a carries I amperes of current. The magnetic field surrounding it is given by H_\phi = \dfrac{I}{2\pi\rho} for \rho > a. Obtain expressions for (i) the magnetic energy stored per unit length in the region b \ge \rho \ge a and (ii) the equivalent inductance L per unit length.

With a suitable diagram, deduce an expression for numerical aperture (NA) for an optical fiber having refractive indices of core and cladding n_1 and n_2, respectively and being placed in a medium of index n_0.

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.

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.

Show that two convex lenses of the same material kept separated by a distance a, which is equal to the average of two focal lengths, may be used as an achromat, that is, a=\frac{1}{2}(f_1+f_2).

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.

What do you mean by underfilled and overfilled conditions with reference to numerical aperture in exciting light in fiber?

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

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.

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}.

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

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}.

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?

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})