Question

A transparent solid cylindrical rod has a refractive index of $\frac { 2 } { \sqrt { 3 } }$. It is surrounded by air. A light ray is incident at the midpoint of one end of the rod as shown in the figure.

The incident angle q for which the light ray grazes along the wall of the rod is -

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

Answer 1

Answer: (D)

$\sin ^ { - 1 } \left( \frac { 1 } { \sqrt { 3 } } \right)$

Answer 2

m_air sin q = m_cylider. sin (90 – q_C)

Ž 1.sin q = $\frac { 2 } { \sqrt { 3 } }$ .cosq_C

Ž sin q = $\frac { 2 } { \sqrt { 3 } }$cos $\left[ \sin ^ { - 1 } \frac { 1 } { \mu _ { \mathrm { cy } } } \right]$

= $\frac { 2 } { \sqrt { 3 } } \cos \left[ \sin ^ { - 1 } \frac { \sqrt { 3 } } { 2 } \right]$

= $\frac { 2 } { \sqrt { 3 } } \cos 60 ^ { \circ }$ = $\frac { 1 } { \sqrt { 3 } }$

Ž q = sin^–1 $\frac { 1 } { \sqrt { 3 } }$ .