Discuss how population inversion is achieved in Ruby laser. What is 'laser spiking'? Why does it occur?

What is axial chromatic aberration? A convex lens has a focal length of 15.5 \times 10^{-2}\,\mathrm{m} for red colour and 14.45 \times 10^{-2}\,\mathrm{m} for violet colour. If an object is kept at a distance of 40\,\mathrm{cm} from the lens, calculate the longitudinal chromatic aberration of the lens.

Discuss the intensity distribution in Fraunhofer diffraction pattern due to a single slit. Obtain conditions for maxima and minima of the intensity distribution. Show that the intensity of the first maxima is about 4.95\% of that of the principal maxima.

Explain the principle and working of He-Ne laser. What is the role of He gas? Why is it necessary to use narrow tube? How many longitudinal modes can be excited for an He-Ne laser in a cavity of length 30 cm and having half width of gain profile of laser material 2 \times 10^{-3}\,\mathrm{nm}? The emission wavelength is 6328\,\mathring{\mathrm{A}}.

A plane transmission grating has 3000 lines in all, having width of 3\ \mathrm{mm}. What would be the angular separation in the first order spectrum of the two sodium lines of wavelengths 5890\mathring{\mathrm{A}} and 5896\mathring{\mathrm{A}}? Can they be seen distinctly?

When the two waves of nearly equal frequencies interfere, then show that the number of beats produced per second is equal to the difference of their frequencies.

What do you mean by spherical aberration of a lens? Show that if two plano-convex lenses are kept at a distance equal to the difference of their focal lengths, the spherical aberration would be minimum.

Distinguish between positive and negative crystals in terms of double refraction. How are these crystals used to make quarter wave plates? Explain how the quarter wave plate is used in producing elliptically and circularly polarized light.

Explain with proper example the interferences due to 'division of wavefront' and 'division of amplitude'.

What is multiple-beam interference? Discuss the advantages of multiple-beam interferometry over two-beam interferometry. Explain the fringes formed by Fabry-Perot interferometer.

Explain the principle of operation of optical fibre. What are the different losses that take place in optical fibre?

Show that the areas of all the half-period zones are nearly the same. Find the radius of 1st half-period zone in a zone plate whose focal length is 50\ \mathrm{cm} and the wavelength of the incident light is 500\ \mathrm{nm}.

Sunlight is reflected from a calm lake. The reflected light is 100% polarized at a certain instant. What is the angle between the sun and horizon?

Find the velocity of sound in a gas in which two waves of wavelengths 1.00\,\mathrm{m} and 1.01\,\mathrm{m} produce 10 beats in 3 seconds.

A plane-polarized light passes through a double-refracting crystal of thickness 40\,\mu\mathrm{m} and emerges out as circularly polarized. If the birefringence of the crystal is 0.00004, then find the wavelength of the incident light.

Obtain the system matrix for a thin lens placed in air and made of material of refractive index 1.5 having radius of curvature 50\,\mathrm{cm} each. Also find its focal length.

How is laser light different from ordinary light? Discuss the working principle of ruby laser. What role do chromium ions play in this process?

In Michelson interferometer, 100 fringes cross the field of view when the movable mirror is displaced through 0.029\,\text{mm}. Calculate the wavelength of the light source used.

Obtain the conditions for constructive interference and destructive interference in a thin film due to reflected light.

The equation of a progressive wave moving on a string is y = 5\sin \pi(0.01x - 2t). In this equation, y and x are in centimetres and t is in seconds. Calculate amplitude, frequency and velocity of the wave. If two particles at any instant are situated 200\,\mathrm{cm} apart, what will be the phase difference between these particles?