Question

Light travels in two media $M_1$ and $M_2$ with speeds $1.5 × 10^8ms^{–1 }$and $2.0 × 10^8ms^{–1}$, respectively. The critical angle between them is:

• A. $tan^{-1}\bigg(\frac{3}{\sqrt7}\bigg)$
• B. $tan^{-1}\bigg(\frac{2}{3}\bigg)$
• C. $cos^{-1}\bigg(\frac{3}{4}\bigg)$
• D. $sin^{-1}\bigg(\frac{2}{3}\bigg)$

Answer 1

Answer: (A)

$tan^{-1}\bigg(\frac{3}{\sqrt7}\bigg)$

Answer 2

**The Critical angle between $M_1$ and **$M_2$

$sin$ $i_c$ = $\frac{μ_2}{μ_1} = \frac{v_1}{v_2}$

$sin$ $i_c$ = $\frac{3}{4}$

$⇒ tan \;i_c$ = $\frac{3 }{ \sqrt{7}}$

$i_c$ = $tan ^{-1}$ = $\frac{3}{\sqrt7}$

Hence, the correct option is (A): $tan^{-1}\bigg(\frac{3}{\sqrt7}\bigg)$