Explain the Laser actions in

(i) Helium Neon Laser

(ii) Gas Laser

How can it be proved experimentally that energy transmission is associated with a wave? The disc of a siren having 60 holes makes 420 revolutions per minute. Find the wavelength of its sound in air 0^\circ\text{C}, if velocity of sound at 0^\circ\text{C} is 332\text{ ms}^{-1}.

For transverse waves passing over a uniform string, prove that the slope of the siring at any position x at a given time is numerically equal to the ratio of the particle speed at that position x and time to the wave speed over the string.

The diameter of the central zone of a zone-plate is 2.3\text{ mm}. If a point source of light (\lambda=589.3\text{ nanometer}) is placed at a distance of 6\text{ metre} from it, calculate the position of the first image.

Write a short note on Spatial and temporal coherence.

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.

Calculate the rate of energy dissipation by a damped harmonic oscillator, in the weak damping limit with \omega_o \tau \gg 1, so that \omega=\omega_o. Symbols have their usual meanings.

If two pipes one closed at one end and the other open at both ends, have fast overtones of the same frequency, what is the ratio of their respective lengths?

Two express trains travelling at 10\text{ km/hour} are meeting each other while one of them is whistling. If the frequency of the note is 800\text{ Hz}, find the apparent pitch as heard by an observer in the other train after they passed each other. Velocity of sound in air = 340\text{ ms}^{-1}.

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}.

Write a short note on Holography.

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?

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.

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.

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.

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 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.

Derive an expression for the resolving power of a diffraction grating.

Write a note on Oscillations with two degrees of freedom.