Question

A ray of light travelling in a transparent medium falls on a surface separating the medium from air at an angle of incidence ${40}^o$. The ray undergoes total internal reflection. If $n$ is the refractive index of the medium with respect to air, select the possible values of $n$ from the following$(Givensin{40}^o=0.64)$

• A. 0.64
• B. 1.5
• C. 1.58
• D. 1.6

Answer 1

Answer: (C), (D)

The correct options are
C 1.6
D 1.58

The angle of incidence of all the rays is ${45}^{\circ }$ at the hypotenuse. For a critical angle of ${45}^{\circ }$ the refractive index must be $sin{45}^{-1}$ = $\sqrt{2}=1.414$

The value of $\mu$ should be greater than 1.414

${\theta }_{critial}=si{n}^{-1}\left(\frac{1}{\mu }\right)$

if $\mu =1.3\Rightarrow {\theta }_{cri}=si{n}^{-1}\left(\frac{1}{1.3}\right)=50.28$

$\mu =1.4\Rightarrow {\theta }_{cri}=si{n}^{-1}\left(\frac{1}{1.4}\right)=45.58$

$\mu =1.5\Rightarrow {\theta }_{cri}=si{n}^{-1}\left(\frac{1}{1.5}\right)=41.8$

$\mu =1.6\Rightarrow {\theta }_{cri}=si{n}^{-1}\left(\frac{1}{1.6}\right)=38.68$

$\therefore$ so 1.5 and 1.6 are possible values.