PYQ Bank

Write down the equation of motion of a weakly damped harmonic oscillator driven by a harmonic force. Obtain an expression for the maximum amplitude of oscillation under steady-state conditions.

A parallel beam of light from a He--Ne laser (\lambda=630 nm) is made to fall on a narrow slit of width 0.2\times10^{-3} m. The Fraunhofer diffraction pattern is observed on a screen placed in the focal plane of a convex lens of focal length 0.3 m. Calculate the distance between the \begin{qroman}\item first two minima and \item first two maxima on the screen.\end{qroman}

Explain the physical significance of resolving power of a grating with relevant mathematical expression.

Consider a zone plate with radii r_n = 0\cdot 11 \sqrt{n}\text{ cm} illuminated by a monochromatic light of wavelength 589\text{ nm}. Calculate the positions of first two foci.

The displacement associated with a three-dimensional plane wave is given by \Psi(x,y,z,t) = a\cos\left[\frac{\sqrt{3}}{2}kx + \frac{1}{2}ky - \omega t\right]. Calculate the angles made by the propagating wave with the x, y and z-axes.

The dispersion relation for deep water waves is given by \omega^2 = gk + ak^3 where g and a are constants. Obtain expressions for phase velocity and group velocity in terms of the wavelength \lambda. \omega and k represent the angular frequency and wave number, respectively.

Classify fibers based on the number of modes that can propagate through them. Depict step-index and graded-index multimode fibers pictorially.

During an earthquake, a horizontal shelf moves vertically. If its motion can be regarded simple harmonic, calculate the maximum value of amplitude of oscillation so that the books resting on it stay in contact with it always. Take g=9.8\ \mathrm{m\,s^{-2}} and T=0.5\ \mathrm{s}.

A plano-convex lens of radius 1\cdot 0\text{ m} is placed on an optically flat glass plate. The space between the lens and the glass plate is filled with a liquid. The diameter of the 5^{\text{th}} ring changes to 3\cdot 0 \times 10^{-3}\text{ m}. Calculate the refractive index of the liquid when the ring is bright. The wavelength of light used is 589\text{ nm}.

Discuss the applications of lasers in communication and medicine.

When two tuning forks were sounded together, 24 beats were produced in 6\text{ seconds}. After loading one tuning fork with wax, they produced 30 beats in 6\text{ seconds}. If the unloaded fork frequency is 512, what is the frequency of the other ?

A body describing simple harmonic motion (SHM) has a maximum acceleration of 8\ \pi\text{m/sec}^2 and a maximum speed of 1\cdot 6\text{ m/sec}. Find the time period (T) and the amplitude (A) of SHM.

The separation between the slits is 0.5\,\text{mm} in Young's double-slit experiment. The interference pattern observed on a screen placed 5\,\text{m} away reveals the location of the first maximum which is 6\,\text{mm} from the centre of the pattern. Calculate the wavelength of light and separation between second and third bright fringes.

Explain mathematically the phenomenon of beats. How does it differ from that of interference ?

What are Einstein's A and B coefficients ? Establish a relation between them.

Explain the Fraunhofer diffraction at a single slit and obtain the condition for minima. Derive the expression for resolving power of a grating.

Show that a travelling wave on the string, clamped on both the ends, undergoes a phase change of \pi. Hence obtain the time-independent form of the wave equation representing a standing wave on the string.

The motion of a damped mechanical oscillator is represented by m\ddot{x}+\alpha\dot{x}+\beta x=0 where m, \alpha and \beta are constants. The oscillator is critically damped. The system is given an impulse at x=0 and t=0, resulting in an initial velocity v. After how much time the system experiences maximum displacement?

Distinguish between Fresnel and Fraunhofer classes of diffraction. Show that the area of each Fresnel half-period zone is same.

A diffraction grating of width 5 cm with slits of width 10^{-4} cm separated by a distance of 2\times10^{-4} cm is illuminated by light of wavelength 550 nm. What will be the width of the principal maximum in the diffraction pattern? Would there be any missing orders?