NCERT Solutions for Class 12 Physics Chapter 10 Wave Optics – PDF Download & Explanations

Ans.10.1 Wavelength of incident monochromatic light,  $\lambda$ = 589 nm = 589  $\times {10}^{-9}$ m

Speed of light in air, c = 3  $\times {10}^8$ m/s

Refractive index of water,  $\mu$ = 1.33

In case of reflection, the ray goes back to the same medium. Hence wavelength, frequency and speed of reflected beam will be same as incident beam.

Frequency of light beam is given by the relation,  $\nu$ =  $\frac{c}{\lambda }$ =  $\frac{3\mathrm{}\times {10}^8}{589\mathrm{}\times {10}^{-9}}$ = 5.09  $\times {10}^{14}$ Hz.

Hence speed = 3  $\times {10}^8$ m/s, Wavelength = 589  $\times {10}^{-9}$ m, Frequency = 5.09  $\times {10}^{14}$ Hz of incident ray and reflected ray will remain unchanged.

(i) Frequency = does not depend on the property of the medium in which it is travelling, hence frequency will remain same, i.e. 5.09  $\times {10}^{14}$ Hz

(ii) Speed of light in water depends upon the refractive index of water, hence speed of light, v =  $\frac{c}{\mu }$ =  $\frac{3\mathrm{}\times {10}^8}{1.33}$ = 0.226  $\times {10}^9$ m/s

Wavelength in water,  $\lambda$ =  $\frac{v}{\nu }$ =  $\frac{0.226\mathrm{}\times {10}^9}{5.09\mathrm{}\times {10}^{14}}$ = 4.432  $\times {10}^{-7}$ m = 443.2 nm

Hence the speed, frequency and wavelength of refracted light are 0.226  $\times {10}^9$ m/s, 5.09  $\times {10}^{14}$ Hz and 443.2 nm

Q.10.2 What is the shape of the wave front in each of the following cases:

(a) Light diverging from a point source.

(b) Light emerging out of a convex lens when a point source is placed at its focus.

(c) The portion of the wave front of light from a distant star intercepted by the Earth.

Ans.10.2 The shape of the wave front in case of a light diverging from a point source is spherical.

The shape of the wave front in case of a light emerging out of a convex lens when a point source is placed at its focus is a parallel grid.

The portion of the wave front of light from a distant star intercepted by the Earth is a plane.

Q.10.3 (a) The refractive index of glass is 1.5. What is the speed of light in glass? (Speed of light in vacuum is 3.0 × 108 m s–1)

(b) Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism?

Ans. 10.3 The refractive index of glass,  $\mu$ = 1.5

Speed of light in vacuum, c = 3.0  $\times {10}^8$ m/s

Speed of light in glass is given by the relation,  $v$ =  $\frac{c}{\mu }$ =  $\frac{3.0\mathrm{}\times {10}^8}{1.5}$ = 2  $\times {10}^8$ m/s

The speed of light in glass is not independent of the colours of light. The refractive index of a violet component of white light is less than the speed of red light in glass. Hence, violet light travels slower than red light in a glass prism.

Ans.10.4 Distance between the slits, d = 0.28 mm = 0.28  $\times {10}^{-3}$ m

Distance between the slits and the screen, D = 1.4 m

Distance between the central bright fringe and the fourth ( n = 4) fringe, u = 1.2 cm

= 1.2  $\times {10}^{-2}$ m

In case of a constructive interference, we have the relation for the distance between two fringes as : u = n  $\lambda \frac{D}{d},$ where n = order of fringes = 4 and  $\lambda$ = wavelength of the light used

Hence,  $\lambda$ =  $\frac{ud}{nD}$ =  $\frac{1.2\mathrm{}\times {10}^{-2}\times 0.28\mathrm{}\times {10}^{-3}}{4\times 1.4}$ = 6  $\times {10}^{-7}$ m = 600  $\times {10}^{-9}$ m = 600 nm

Hence, wavelength of the light is 600 nm.