MCQ
A transparent solid cylindrical rod has a refractive index of $\frac{4}{\sqrt {3}}$ It is surrounded by a medium of refractive index $2$. A light ray is incident at the mid-point of one end of the rod as shown in the figure.

The incident angle $\theta $ for which the light ray grazes along the wall of the rod is

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

Answer

Correct option: B.
${\sin ^{ - 1}}\left( {\frac{2}{{\sqrt 3 }}} \right)$
b
$\sin \theta=\frac{4}{\sqrt{3}} \sin r$

$\sin (90-r) \times \frac{4}{\sqrt{3}}=\sin 90 \times 2$

$\cos r=\frac{\sqrt{3}}{2}$

$r=30^{\circ}$

$\sin \theta=\frac{4}{\sqrt{3}} \sin 30^{\circ}$

$\sin \theta=\frac{2}{\sqrt{3}}$

$\theta=\sin ^{-1} \frac{2}{\sqrt{3}}$

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