PYQ Bank

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.

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}}.

Calculate the focal lengths of the components of an achromatic telescope objective having a power of +3\cdot 333 diopter, made from crown glass and flint glass, whose dispersive powers are 0\cdot 012 and 0\cdot 02 respectively.

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.

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.

(i) What is population inversion? How is it efficiently achieved in He-Ne laser? Show it with necessary energy levels diagram.

(ii) Show that for a normal optical source emitting at 600\text{ nm} at a temperature of 10^3\text{ K}, the spontaneous emission dominates over stimulated emission.

Thin transparent films produce colours when a white light falls on them or they act as antireflecting coatings. Find the conditions for these characteristics.

(i) When a monochromatic light passes through a single slit, dark and bright fringes are observed on a screen kept far away from the slit. Draw an amplitude and intensity pattern of the light on the screen.

(ii) Write an expression for intensity distribution and give the conditions for bright and dark fringes.

(iii) If the slit width is 0\cdot 3\text{ mm} and the distance between the screen and the slit is about 30\text{ cm}, then what is the angle of diffraction for the first minimum? (\lambda = 5 \times 10^{-5}\text{ cm})

(i) Give the equation of motions for a particle executing simple harmonic motion for undamped, damped and forced vibrations, and explain the terms.

(ii) Give a plot between the displacement and time for each case of the above and interpret.

(iii) What are the conditions for critical damping and resonance?

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.

(i) How are linearly polarised and circularly polarised lights generated from unpolarised light and are analysed?

(ii) A calcite crystal is to be used for producing a quarter wave plate. The refractive indices of the crystal for ordinary ray and extraordinary ray are 1\cdot 65836 and 1\cdot 48641 respectively. What is the thickness of the plate required if the light of wavelength 632\cdot 8\text{ nm} is to be used?

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.

State and explain Fermat's principle of extremum path and use the same to deduce the laws of reflection and refraction of light.

Discuss the properties of Cornu spiral. Show that the spiral can be used to obtain the intensity distribution in the Fresnel's diffraction pattern due to a straight edge.

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}.

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

(i) In a Michelson's interferometer, 100 fringes cross the field of view when the movable mirror is displaced through 2\cdot 894 \times 10^{-3}~\text{cm}. Calculate the wavelength of the monochromatic source of light. (ii) A shift of 200 fringes is observed when the movable mirror of a Fabry-Pérot interferometer is shifted by 0\cdot 0298~\text{mm}. Calculate the wavelength of the incident radiation.

Discuss absorption loss in an optical fibre comparing and contrasting the intrinsic and extrinsic absorption mechanisms.

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

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.