PYQ Bank

Give a mathematical analysis of forced vibration and hence explain the phenomenon of amplitude resonance.

Show that the particle velocity in case of a plane progressive wave is given by \frac{\partial y}{\partial t} = -V \frac{\partial y}{\partial x} (where V is the wave velocity). Hence obtain the differential equation of wave motion.

A particle executing simple harmonic motion, has an acceleration (\pi^2/3)\text{ cm/sec}^2 when the displacement is 1\text{ cm}. Determine the period.

State Rayleigh Criterison for limit of resolution. Show that \frac{I_{\text{middle}}}{I_{\text{max}}} = \frac{8}{\pi^2}

A diffraction grating with 3 \times 10^4 lines is used in the second order in the range of wavelength 6000\text{\AA}. Find the smallest \Delta\lambda it can resolve.

Distinguish between Fresnel and Fraunhofer classes of diffraction of light. Discuss the theory of a plane grating and hence find an expression for the angular dispersion of a plane grating.

The phase velocity of surface waves of wavelength \lambda is v_p = \left( \frac{2 \pi T}{\lambda \rho} + \frac{g \lambda^{1/2}}{2 \pi} \right) where T is the surface tension and \rho the density of the liquid and g is acceleration due to gravity. Find the group velocity and express it in terms of the phase velocity. For which wavelength is the phase velocity a minimum ?

Define geometrical resolving power of an optical instrument. Derive the expression for the resolving power of a microscope and comment on the relation between resolving power and magnifying power, if any exists.

Deduce an expression for the diffraction waves at single slit and discuss how it is related with a Fourier transform.

A soap film of refractive index 1.33 is illuminated with light of different wavelength at an angle of 45^\circ. There is complete destructive interference for \lambda = 5890\text{\AA}. Find thickness of the film.

Explain the laws of refraction of light on the basis of Huygens principle.

A particle of mass 10 g lies in a potential given by V(x) = 32 x^2 + 0.2 where x is in metres and V(x) in joules. Write down the equation of motion and solve it. What is the frequency of oscillation?

Write a note on Purity of spectral lines and coherence length.

Deduce the possible thickness of a quarter wave plate of quartz which is to be used for sodium light of wavelength 5890 \text{\AA}, (\mu_o = 1.558, \mu_e = 1.486.)

Write a note on He-Ne laser.

What is hologram? Explain how the image of the object is formed when one looks through it.

Write a note on Rayleighs criterion and resolving power of a telescope.

For a certain wave, system the angular velocity \omega and the wave vector k are related as follows: \omega = \omega_0 \left| \sin \frac{k a}{2} \right| \quad \text{for } -\frac{\pi}{a} < k < \frac{\pi}{a} Determine and plot the phase velocity and the group velocity for this system.

A single, slit of width 0.14\text{ mm} is illuminated normally by monochromatic light and diffraction bands are observed on a screen 2\text{ m} away. If the centre of the second dark band is 1.6\text{ cm} from the middle of the central bright band deduce the wavelength of light.

Show schematically the intensity distribution for a 2-slit Fraunhofer diffraction-interference, if slit-widths are 2\lambda each and centres of slits have separation 6\lambda. Assume incident light falling normally, and limit the discussion to the central diffraction band range.