Question

A ray of light travels from a denser to a rarer medium. After refraction, it bends away from the normal. When we keep increasing the angle of incidence, the angle of refraction also increases till the refracted ray grazes along the interface of two media. The angle of incidence for which it happens is called critical angle. If the angle of incidence is increased further the ray will not emerge and it will be reflected back in the denser medium. This phenomenon is called total internal reflection of light.

(i) A ray of light travels from a medium into water at an angle of incidence of 18. The refractive index of the medium is more than that of water and the critical angle for the interface between the two media is 20⁰. Which one of the following figures best represents the correct path of the ray of light?

(ii) For which of the following media, with respect to air, the value of critical angle is maximum?

(a) Crown glass

(b) Flint glass

(c) Water

(d) Diamond

(iii) The critical angle for a pair of two media A and B of refractive indices
2.0 and 1.0 respectively is:

(a) 0°

(b) 30°

(c) 45°

(d) 60⁰

(iv) The critical angle of pair of a medium and air is 30°. The speed of light in the medium is:

(a) 1 x 10⁸ m s^-1

(b) 1.5 x 10⁸ m s^-1

(c) 2.2 x 10⁸ m s^-1

(d) 2.8 × 10⁸ m s^-1

Answer 1

(i) When a ray of light travel from denser to rarer medium, the refracted ray bonds away from the natural 

Correct option is (A)

(ii) Critical angle \(\theta = sin^{-1}\left(\frac{n_{air}}{n_{water}}\right)\)

\(\theta = sin^{-1}\left(\frac1{1.33}\right)\)

\(\theta = 48.75^\circ\)

Correct option is (c) water

(iii) Critical angle \(\theta = sin^{-1}\left(\frac{n_2}{n_1}\right)\)

\(\theta = sin^{-1}\left(\frac1{2}\right)\)

\(\theta = sin^{-1}\left(sin30^\circ\right)\)

\(\theta = 30^\circ\)

Correct option is (b) 30°

(iv) \(\theta = sin^{-1}\left(\frac1x\right)\)

\(sin\,\theta = \frac1{x}\)

\(x= \frac1{sin\,30^\circ}\)

x = 2

\(x = \frac c{v_m}\)

\(v = \frac{c}{x}\)

\(v = \frac{3\times10^8}{2}\)

v = 1.5 x 10⁸ m/s

Correct option is (b) 1.5 x 10⁸ m/s