Question

Light is incident from a medium into air at two possible angles of incidence $(A) 20^{\circ}$ and $(B) 40^{\circ}$. In the medium light travels $3.0 \,cm$ in $0.2\, ns$. The ray will :

• A. suffer total internal reflection in both cases (A) and (B)
• B. suffer total internal reflection in case (B) only
• C. have partial reflection and partial transmission in case (B)
• D. have 100% transmission in case (A)

Answer 1

Answer: (B)

Velocity of light in medium
$V_{med} = \frac{3\,cm}{0.2ns} = \frac{3\times10^{-2}m}{0.2\times10^{-9}s} = 1.5\,m/s$
Refractive index of the medium
$\mu = \frac{V_{air}}{V_{med}} = \frac{3\times10^{8}}{1.5} = 2\, m/s$
As$\,\mu = \frac{1}{sin\,C}$
$\therefore \,sin\,C = \frac{1}{\mu} = \frac{1}{2} = 30^{\circ}$
Condition of TIR is angle of incidence i must be greater than critical angle. Hence ray will suffer TIR in case of $\left(B\right) \left(i = 40^{\circ} > 30^{\circ}\right)$ only.