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 $3.0cm$ in $0.2ns$. 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
$V_{med}=\frac{3cm}{0.2ns}=\frac{3\times 10^{-2}m}{0.2\times 10^{-9}s}=1.5m/s$
Refractive index of the medium
$\mu =\frac{V_{air}}{V_{med}}=\frac{3\times 10^8}{1.5}=2m/s$
As$\mu =\frac{1}{sinC}$
$\therefore sinC=\frac{1}{\mu }=\frac{1}{2}=30^{\circ }$
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.