Question

A plane mirror is placed horizontally inside liquid of refractive index $7/5$ . As ray is made incident normally on the mirror it is rotated through angle $\theta .$ The value of $\theta $ for which ray does not come out of the liquid surface is $\theta >\frac{1}{2}\left(sin\right)^{- 1}\left(\right.\frac{x}{7}\left.\right)$ where $'x'$ has the value____.

Answer 1

As plane mirror is rotated through angle $\theta ,$ the reflected ray turns through angle $2\theta .$ For total internal reflection to take place at liquid-air boundary, $sin2\theta >sini_{c}$
$sin2\theta >\frac{1}{\mu _{d}}$ i.e.,
$sin2\theta >\frac{1}{7 / 5}$
$2 \theta>\sin ^{-1}(5 / 7)$
$\theta>\frac{1}{2} \sin ^{-1}(5 / 7)$
$\Rightarrow x=5$