PYQ Bank

What do you understand by quarter wave plate? How can it be used to convert a linearly polarized wave into a circularly polarized wave?

Consider the formation of Newton's rings when two closely spaced wavelengths are present, for example, the \text{D}_1 and \text{D}_2 lines of sodium (\lambda_1 = 5890\text{ \AA} and \lambda_2 = 5896\text{ \AA}). What will be the effect of the presence of these two wavelengths as the lens is gradually moved away from the plate? What will happen if the sodium lamp is replaced by a white source? (The radius of curvature of the lens, R = 100\text{ cm})

A glass chamber 25\text{ mm} long filled with air is positioned in front of one of the secondary sources in Young's experiment. The air is removed from the chamber and a test gas is entered in its stead. On comparing the fringe system corresponding to air with that of the test gas, it is found that the entire interference pattern on the screen was displaced by 21 bright bands towards gas-containing chamber. Given that \lambda = 656{\cdot}2816\text{ nm} for which the refractive index of air is n_a = 1{\cdot}000276. Determine the refractive index of the gas (n_g).

The quality factor Q in a damped harmonic motion is defined as Q = \frac{2\pi \times \text{Average energy stored per cycle}}{\text{Average energy dissipated per cycle}} Show that Q = \frac{\omega}{2b} (where the symbols have usual meaning).

Why is population inversion in general not possible in a two-level laser system? Explain it.

What is axial chromatic aberration? A convex lens has a focal length of 15.5 \times 10^{-2}\,\mathrm{m} for red colour and 14.45 \times 10^{-2}\,\mathrm{m} for violet colour. If an object is kept at a distance of 40\,\mathrm{cm} from the lens, calculate the longitudinal chromatic aberration of the lens.

Prove that when light goes from one point to another via a plane mirror, the path followed by light is the one for which the time of flight is the least.

It is required that a real image twice the size of the object be formed by a thin plano-convex lens. If the lens has a radius of curvature of 50\text{ cm} and a refractive index of \mu = 1\cdot 5, determine the locations of the object and image with respect to the lens.

With a neat ray diagram, describe Fraunhofer diffraction at a circular aperture.

In an \text{He}-\text{Ne} laser system, the two energy levels of \text{Ne} involved in lasing action have energy values of 20\cdot 66\text{ eV} and 18\cdot 70\text{ eV} respectively. Population inversion occurs between these two energy levels. What will be the wavelength of the laser beam produced ? What will be the population in the metastable energy level with respect to the upper excited level at room temperature (27^\circ\text{C}) ?

Explain Huygens' theory of double refraction in a uniaxial crystal. Discuss the formation of ordinary and extraordinary rays for oblique incidence when an optic axis is in the plane of incidence and when it is perpendicular to the plane of incidence.

How can one convert a left-handed circularly polarised light into a right-handed one (and vice versa)? Calculate the thickness of a quarter-wave plate when the wavelength of light is 589\,\mathrm{nm}. Given: \mu_0 = 1.544 and \mu_E = 1.553.

What are the fringes of equal thickness and fringes of equal inclination? In a Newton's ring arrangement with a source emitting two wavelengths \lambda_1=6\times10^{-7}\,\text{m} and \lambda_2=5.9\times10^{-7}\,\text{m}, it is found that the m^{\text{th}} dark ring due to one wavelength coincides with the (m+1)^{\text{th}} dark ring due to the other. Find the diameter of the m^{\text{th}} dark ring, if the radius of curvature of the lens is 90\,\text{cm}.

A High Frequency (HF) radio receiver receives simultaneously two signals from a transmitter 400\text{ km} away, one by a path along the surface of the Earth, and the other by reflection from a portion of the ionospheric layer situated at a height of 200\text{ km}. We assume that the Earth is flat and the ionospheric layer acts as a perfect horizontal reflector, which is moving slowly in the vertical direction. When the frequency of the transmitted wave is 10\text{ MHz}, it is observed that the combined signal strength varies from maximum to minimum and back to maximum 6 times per minute. With what slow vertical speed is the ionospheric layer moving ?

Two Fabry -- Pérot interferometers have same plate separation but the coefficients of intensity reflection are 0\cdot 7 and 0\cdot 9. Deduce the relative width of the maxima in the above two cases.

Discuss how population inversion is achieved in Ruby laser. What is 'laser spiking'? Why does it occur?

How can the refractive index of a liquid be determined using a method of Newton's rings ? Obtain an appropriate expression for calculating the refractive index.

In what way is holography different from conventional photography? Discuss the salient features of a hologram. What are the requirements for the formation and reading of a hologram?

Thin transparent films produce colours when a white light falls on them or they act as antireflecting coatings. Find the conditions for these characteristics.

What do you mean by spherical aberration of a lens? Show that if two plano-convex lenses are kept at a distance equal to the difference of their focal lengths, the spherical aberration would be minimum.