PYQ Bank

Consider a thick lens of thickness t made of a material of relative refractive index n. Let R_1 and R_2 be the radii of curvature of its two surfaces. Obtain the system matrix of the lens.

Describe the interference by a plane parallel thin film when illuminated normally and obliquely by a plane wave. Also list some important practical applications of the thin film interference phenomenon.

Consider a laser system consisting of an active medium placed between a pair of mirrors forming a resonator. Obtain an expression for the threshold population inversion required for the oscillations of laser.

A 15\cdot 0\text{ cm} violin string, fixed at both the ends, is vibrating with the largest wavelength. The speed of the wave in this string is 250\text{ m/s}, and the speed of sound in air is 350\text{ m/s}. What is the frequency and wavelength of the emitted sound wave?

Consider a 10\text{ mW} laser beam passing through a 50\text{ km} fiber link of attenuation 0.5\text{ dB/km}. Calculate the power of the laser at the end of the link.

A three-level laser system emits laser light at a wavelength of 550\text{ nm}. If the population of the upper level exceeds that of the lower level by 25\%, determine the negative temperature characterizing the system.

Consider a thin lens combination of two convex lenses of focal lengths f_1 = +10\text{ cm} and f_2 = +20\text{ cm}, respectively, separated by 25\text{ cm}. Determine the focal length of the combination and the positions of unit planes.

Explain the phenomenon of double-refraction in calcite crystal with special reference to Ordinary Ray (OR), Extraordinary Ray (ER) and uniaxial negative crystal.

(i) What are the similarities and dissimilarities between a zone plate and a convex lens ? (ii) A monochromatic light of wavelength 5860 \times 10^{-8}\text{ cm} is incident normally on a 2\text{ cm} wide grating. The first order spectrum is produced at an angle of 20^\circ with respect to the normal. Determine the total number of lines on the grating. How does the resolving power of grating depend on the number of rulings on the grating ?

(i) Distinguish between interference fringe pattern and diffraction fringe pattern. (ii) In an experiment using Newton's rings, the diameter of 5^{\text{th}} and 15^{\text{th}} rings were found to be 33.6 \times 10^{-4}\text{ m} and 59 \times 10^{-4}\text{ m} respectively. Calculate the radius of curvature of the plano-convex lens if the source of light is sodium light (\lambda = 589.0\text{ nm}). Mention any other applications of Newton's ring experiment.

Explain the phenomenon of double refraction. What are positive and negative crystals? Give their examples.

The diameter of central zone of a zone plate is 2.4\text{ mm}. If a point source of light of wavelength 600\text{ nm} is placed at a distance of 5.0\text{ m} from the zone plate, calculate the position of the first image.

What do you understand by optical activity? A linearly polarized light is propagating along the optic axis of a quartz crystal of thickness 0.2\text{ cm}. If the difference in the refractive indices corresponding to right circularly polarized and left circularly polarized beams is 7 \times 10^{-5} and the wavelength of the light is 0.5\text{ }\mu\text{m}, calculate the angle of polarization.

Write down the system matrix for a combination of two thin lenses in paraxial approximation. Hence obtain the focal length of the combination and the positions of unit planes.

Calculate the group and phase velocities for the wave packet corresponding to a relativistic particle.

Consider a damped harmonic oscillator given by the equation \ddot{x} + 2\mu \dot{x} + \omega_0^2 x = 0. Obtain the displacements for (i) overdamped, (ii) underdamped and, (iii) critically damped motion.

A telescope has an objective lens of diameter 10\text{ cm}. Determine whether this telescope can resolve two stars having an angular separation of 2\cdot 4 seconds of arc. (Assume the wavelength of starlight as 550\text{ nm})

A weakly damped harmonic oscillator consisting of spring-mass system has the following parameters : Mass m = 0.25\text{ kg}, Spring constant k = 100\text{ N m}^{-1}, Damping coefficient \gamma = 1\text{ N s m}^{-1} A periodic force F = 5 \cos \omega t (newton) is applied to the system. Determine (i) the amplitude of the oscillator at resonance and (ii) the Q-value of the oscillator.

The intensity at the central maximum observed on a screen in a double-slit experiment is 2 \times 10^{-3}\text{ W/m}^2. If the path difference between interfering waves reaching a point on the screen is \frac{\lambda}{6}, where \lambda is the wavelength of the light used in the experiment, determine the intensity at that point.

What do you understand by attenuation in optical fibers? What are the factors responsible for the attenuation?