Monochromatic light of wavelength 589 nm is incident from air on a water surface. What are the wavelength, frequency and speed of (a) reflected, and (b) refracted light?Refractive index of water is 1.33.

What is the shape of the wavefront in each of the following cases: (I) Light diverging from a pointsource. (II) Light emerging out of a convex lens when a point source is placed at itsfocus. (III) The portion of the wavefront of light from a distant star intercepted by theEarth.

(I) Therefractiveindexofglassis1.5.Whatisthespeedoflightinglass?Speedof light in vacuum is 3.0 × 10⁸ ms^-1) (II) Isthespeedoflightinglassindependentofthecolouroflight?Ifnot,whichofthe two colours red and violet travels slower in a glassprism?

In a Young’s double-slit experiment, the slits are separated by 0.28 mm and the screen is placed 1.4 m away. The distance between the central bright fringe and the fourth bright fringe is measured to be 1.2 cm. Determine the wavelength of light used in the experiment.

In Young’s double-slit experiment using monochromatic light of wavelength?, the intensity of light at a point on the screen where path difference is ?, is K units. What is the intensity of light at a point where path difference is ? /3?

A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment. (I) Findthedistanceofthethirdbrightfringeonthescreenfromthecentralmaximum for wavelength 650 nm. (II) Whatistheleastdistancefromthecentralmaximumwherethebrightfringesdueto both the wavelengthscoincide?

In a double-slit experiment the angular width of a fringe is found to be 0.2° on a screen placed 1 m away. The wavelength of light used is 600 nm. What will be the angular width of the fringe if the entire experimental apparatus is immersed in water? Take refractive index of water to be 4/3.What is the Brewster angle for air to glass transition? (Refractive index of glass = 1.5.)

Light of wavelength 5000 Å falls on a plane reflecting surface. What are the wavelength and frequency of the reflected light? For what angle of incidence is the reflected ray normal to the incident ray?

Estimate the distance for which ray optics is good approximation for an aperture of 4 mm and wavelength 400 nm.

The6563Ålineemittedbyhydrogeninastarisfoundtoberedshiftedby15Å. Estimate the speed with which the star is receding from theEarth.

Explain how Corpuscular theory predicts the speed of light in a medium, say, water, to be greater than the speed of light in vacuum. Is the prediction confirmed by experimental determination of the speed of light in water? If not, which alternative picture of light is consistent with experiment?

You have learnt in the text how Huygens’ principle leads to the laws of reflection and refraction. Use the same principle to deduce directly that a point object placed in front of a plane mirror produces a virtual image whose distance from the mirror is equal to the object distance from the mirror.

Let us list some of the factors, which could possibly influence the speed of wave propagation: (I) Nature of thesource. (II) Direction ofpropagation. (III) Motion of the source and/orobserver. (IV) Wavelength. (V) Intensity of thewave. On which of these factors, if any, does (VI) The speed of light in vacuum, (VII) The speed of light in a medium (say, glass or water),depend?

For sound waves, the Doppler formula for frequency shift differs slightly between the two situations: (i) source at rest; observer moving, and (ii) source moving; observer at rest. The exact Doppler formulas for the case of light waves in vacuum are, however, strictly identical for these situations. Explain why this should be so. Would you expect the formulas to be strictly identical for the two situations in case of light travelling in a medium?

In double-slit experiment using light of wavelength 600 nm, the angular width of a fringe formed on a distant screen is 0.1º. What is the spacing between the two slits?

Two towers on top of two hills are 40 km apart. The line joining them passes 50 m above a hill halfway between the towers. What is the longest wavelength of radio waves, which can be sent between the towers without appreciable diffraction effects?

A parallel beam of light of wavelength 500 nm falls on a narrow slit and the resulting diffraction pattern is observed on a screen 1 m away. It is observed that the first minimum is at a distance of 2.5 mm from the centre of the screen. Find the width of the slit.

In deriving the single slit diffraction pattern, it was stated that the intensity is zero at angles of n?/a. Justify this by suitably dividing the slit to bring out the cancellation.