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A thick wire of mass per unit length m, density p, and Young’s Modulus E, is stretched between two supports and has a tension T. Obtain from first principles an expression for the velocity of longitudinal waves in the wire. Write down the equivalent expression for velocity of transverse waves in the same wire.
Write a short note on Spatial and temporal coherence.
Show that the resolving power of a diffraction grating used with light of wavelength \lambda at normal incidence is W \sin \theta/\lambda, where W is the total width of the grating \theta the angle of diffraction.
The above expression shows that, for given W, \theta and \lambda, the resolving power is independent of number of grooves on the grating. Why do most diffraction gratings have several hundred grooves per mm?
A beam of linearly polarised light is changed into circularly polarised light by passing it through a slice crystal 0.003\text{ cm} thick. Calculate the difference in refractive index of two rays in crystal assuming this to be minimum thickness that will produce the effect and that the wavelength of light is 6 \times 10^{-7}\text{ m}.
The speeds v of waves on the surface of a liquid is given by v = \sqrt{\frac{TK}{P} + \frac{g}{k}} where T is the surface tension of the liquid of density P > K = 2\pi / \lambda, \lambda being the wavelength of the wave and g is acceleration due to gravity Find the wavelength and frequency of waves on water which move with minimum speed.
Write a note on Oscillations with two degrees of freedom.
Derive an expression for the resolving power of a diffraction grating.
Fourier analyse the step-function f(x) = 1 \text{ for } 0 < x < \pi = -1 \text{ for } \pi < x < 2\pi and hence prove that 1 + \frac{1}{9} + \frac{1}{25} + \frac{1}{49} + \dots = \frac{\pi^2}{8}
The equation for displacement of point on a damped oscillator is given by x - 5e^{-0.2t} \sin \frac{\pi}{2}t \text{ metre} Find the velocity of the oscillating point at t = \frac{T}{4} and T_p where T is the time-period of the oscillator.
A beam of light of wavelength 5.82 \times 10^{-7}\text{ m} falls normally on a glass wexge with the wedge angle of 20''. If the refractive index of glass is 1.5, find the number of dark interference fringes per centimetre of the wedge length.
State Huygen's principle and on its basis establish Snell's law of refraction of light. How does the result differ from what Newton's Corpuscular theory gave?
Monochromatic light of wavelength due to diffraction, and critically; comment on \textit{[Source text is incomplete in the available scan.]}
Plane waves pass through a slit whose plane is parallel to the wave fronts. Obtain an expression for the angular spread of the central maximum due to diffraction, and critically comment on the result.
Monochromatic light of wavelength 6.56 \times 10^{-7}\text{ m} falls normally on a grating 2.00\text{ cm} wide. The first order spectrum is produced at an angle of 18^\circ15' from the normal. Deduce the total number of lines in the grating.
How can one produce (i) left-handed circular motion, and (ii) right-handed circular motion by combining two simple harmonic motions? Justify, your answers.
Parallel light is incident normally on diffraction grating having 6,000 lines per cm. Find the angular separation between the maxima for wavelengths 5,890 \text{\AA} and 5,896 \text{\AA} in the second order.
Write a note on Uses of multiple beam interferometry.
What is stimulated emission of light? How does it differ from spontaneous emission? Name any device basal on the stimulated emission of light and explain its working.
Using Huyghens' construction, discuss the propagation of O and E waves in a biaxial crystal when the optic axis is perpendicular to the plane of incidence and parallel to the boundary surface. Take the incident ray to be oblique.