Question

Find the value of $\theta$ in the given figure.

• A. ${\sin }^{-1}$ $\left(\frac{2}{\sqrt{3}}\right)$
• B. $si{n}^{-1}(\frac{1}{\sqrt{3}})$
• C. $si{n}^{-1}(\frac{1}{2})$
• D. $si{n}^{-1}(\frac{1}{\sqrt{2}})$

Answer 1

Answer: (B)

For total internal reflection, $\mu$ $=\frac{1}{sinc}$
where, C = critical angle
Condition for TIR, the angle of incidence must be greater than critical angle C,
($90-{\theta }_1)>C$
sin ($90-{\theta }_1)>sinC$
$cos{\theta }_1$ $=\frac{1}{\mu }$
$cos{\theta }_1$ $>\frac{1}{2/\sqrt{3}}$
$cos{\theta }_1>\frac{\sqrt{3}}{2}$
${\theta }_1>30^{\circ }$
According to Snell’s law,
${\mu }_{1}sin\theta ={\mu }_{2}sin{\theta }_1$
$1sin\theta =\frac{2}{\sqrt{3}}sin{\theta }_1$
$sin\theta =\frac{2}{\sqrt{3}}sin30^{\circ }$
$sin\theta ;=\frac{1}{\sqrt{3}}$
So,
$\theta ;=si{n}^{-1}\left(\frac{1}{\sqrt{3}}\right)$