23. A ray of light travelling in a transparent medium of refractive index μ, falls on a surface separating the medium from air at an angle of incidence of 45° .For which of the following value of μ the ray can undergo total internal reflection ?

23. A ray of light travelling in a transparent medium of refractive index μ, falls on a surface separating the medium from air at an angle of incidence of 45° .For which of the following value of μ the ray can undergo total internal reflection ?

(a) μ = 1.33

(b) μ = 1.40

(c) μ = 1.50

(d) μ = 1.25

Answer :  (c) μ = 1.50

As \( \mu \uparrow \), \( i_c \downarrow \), so \( i > i_c \), so total internal reflection happens

As \( \mu \downarrow \), \( i_c \uparrow \), so \( i < i_c \), no total internal reflection happens

\( 45^\circ < 48^\circ \)

\( \sin i_c = \frac{1}{\mu} \)

\( \sin 45^\circ = \frac{1}{\mu} \)

\( \frac{1}{\sqrt{2}} = \frac{1}{\mu} \)

\( \mu = \sqrt{2} = 1.414 \)