$(a)\;\frac{5}{2} \\ (b)\;\sqrt {\frac{5}{2}} \\ (c)\;\sqrt {\frac{3}{2}} \\ (d)\;\frac{3}{2} $

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$\large\frac{\sin i}{\sin r}=\frac{1}{\mu}$

$\large\frac{\Large\frac{x}{\sqrt{x^2+4h^2}}}{\Large\frac{2h-x}{\sqrt {(2h-x)^2+h^2}}}=\frac{1}{\mu}$----(1)

$\sin r=\large\frac{2h-x}{\sqrt {(2h-x)^2+h^2}}=\frac{x}{h}$---(2)

using (1) and (2)

$\mu =\sqrt {\large\frac{5}{2}}$

Hence b is the correct answer.

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