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A ray of light is incident normally on the first refracting face of the 'prism of refracting angle A. The ray of light comes out at grazing
emergence. If one half of the prism (shaded position) is knocked off, the same ray will

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Emerge at an angle of emergence $\sin^{- 1} (\frac{1}{2} \sec A/2)$

Not emerge out of the prism

Emerge at an angle of emergence $\sin^{- 1} (\frac{1}{2} secA / 4)$

None of these

answer is A.

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Detailed Solution

$\begin{array}{l} μsinA = 1 \times \sin 90 ° \Rightarrow μ = \frac{1}{sinA} \\ andμsin \frac{A}{2} 1 \times sine = \frac{1}{sinA} \times \sin \frac{A}{2} = sine \end{array}$

$sine = \frac{\sin \frac{A}{2}}{2 \sin \frac{A}{2} \cos \frac{A}{2}} \Rightarrow e = \sin^{- 1} [\frac{1}{2} \sec \frac{A}{2}]$

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