A transparent solid cylindrical rod has a refractive index of 2√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.θ The incident angle θ for which the light ray grazes along the wall of the rod is

$sin space to the power of minus space open parentheses 1 half close parentheses$
$sin space to the power of minus space open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses$
$sin space to the power of minus space open parentheses fraction numerator 2 over denominator square root of 3 end fraction close parentheses$
$sin space to the power of minus space open parentheses fraction numerator 1 over denominator square root of 3 end fraction close parentheses$

Solution

sin space to the power of minus space open parentheses fraction numerator 1 over denominator square root of 3 end fraction close parentheses

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