How does Doppler effect of light of relativistic physics qualitatively differ from its non-relativistic analogue ? Calculate the Doppler shift in the frequency of a photon travelling along the y-axis. with respect to an observer moving along the x-axis with a constant speed v.
An ideal massless spring of force constant k has a mass m attached to one of its ends, the other and being fixed to a rigid support. The spring is horizontal floor, A resistive force -bv, proportional to the velocity v acts on the mass. Assuming the damping to be light, obtain the frequency of oscillation. When m = 0.1\text{ kg} and k = 10\text{ N/m}, it is found that the frequency of oscillation is \sqrt{1/2} times the frequency in the absence of damping. Calculate the value of the constant b.
Two transverse harmonic waves, each of amplitude 5mm, wavelength 1m and speed 3 m/s are travelling in opposite directions along a stretched string fixed at both ends. Obtain an expression for the standing wave Produced. Locate the position at the nodes and antinodes.
Discuss the Fresnel diffraction pattern formed by a straight edge using the Cornu's spiral.
The phase velocity of the surface wave in a liquid of surface tension T and density \rho is given by u_p = \sqrt{\frac{g\lambda}{2\pi} + \frac{2\pi T}{\lambda\rho}} Show that the group velocity u_g of the surface wave is given by u_g = \frac{g + (12\pi^2 T) / \rho\lambda^2}{2\sqrt{\left(\frac{2\pi g}{\lambda} + \frac{8\pi^3 T}{\rho\lambda^3}\right)}}
Derive the expression for resolving power of a diffraction grating with N lines. Calculate the minimum number of lines in the diffraction grating if it has to resolve the yellow lines of sodium (589.0\text{ nm} and 589.6\text{ nm}) in the first order.
In an experiment using a Michelson interferometer, explain with the help of suitable ray diagrams.
(i) Why do we need extended source of light,
(ii) Why do we get circular fringes, and
(iii) Shifting of fringes inwards or outwards as we shift the movable mirror.
A wave is represented by \Psi_1 = 10 \cos(5x - 25t). Find wavelength \lambda, velocity v, frequency f and the direction of propagation. If it interferes with another was given by \psi_2 = 20 \cos(5x + 25t + \pi/3), find the amplitude and the phase of the resultant wave. (All dimensions are in SI system).
Show that the motion of a classical particle is analogous to the motion of a wave packet, which can be constructed by superposition of a large number of plane waves. Construct such a wave packet and derive an expression for its group velocity.
How do you know that the light is a transverse wave? What is a quarter wave plate? How is it constructed?
State Fermat's principle. Apply it to get the laws of reflection from a plane surface.
Monochromatic light from a distance source of wavelength \lambda falls on a double slit. A glass plate of thickness t is inserted between one slit and the screen. Calculate the intensity at the central point as the function of thickness t.
Why does one get polarised light from a Nicol's prism? How should one adjust the polariser and analyser, so that an intensity of the incident light is reduced by a factor of 0.25?
A parallel laser beam is incident perpendicularly on a photographic plate. An object is placed at a distance a in front of the photographic plate. Discuss the recording from the plate. If the plate is illuminated by the same light, what is expected and why?
Certain string has a linear mass density of 0.25\text{ kgm}^{-1} and stretched with a tension of 25 N. One end is given a sinusoidal motion, its frequency 5 Hz and amplitude 0.01 metre. If at t = 0, the end has zero displacement and is moving along the positive Y direction, derive the wave speed, the wavelength and the wave equation of the wave in the string.
The phase velocity in a material is \sqrt{g/k} where k is the propagation constant. Prove that the group velocity will be half of the phase velocity.
Parallel rays fall on circular aperture of diameter 1 mm. At a certain position of the screen one gets a dark spot on an axial point. When the screen is moved by 12.5 cm, one again gets a dark spot. Determine \gamma (wavelength).
Show that Simple Harmonic Motion can he described as the projection on its diameter of a uniform circular motion.
Four perfect polarizing plates are stacked so that the axis of each is turned 30 clockwise with respect to the preceding plate: the last plate is crossed with the first. How much of the intensity of an incident unpolarized light is transmitted by the stack ?
How does the resolving power of a microscope differ from that of a telescope ? Find the resolving power of an electron microscope that uses 15\text{ Key} electrons, assuming that this is equal to the electron wavelength.
