Question

Two plane mirrors each $16m$ long are facing each other. The distance between the mirrors is $20cm$. A light incident on one end of one of the mirrors at an angle of ${30}^{\circ }$. How many times is the ray reflected before it reaches the other end ?

Answer 1

$\tan {30}^{\circ }=\left(\frac{x}{20}\right)$
Every reflection sends the ray below by $x$.
$nx<16$
$n.\tan {30}^{\circ }\times 20<16$
$n\left(\frac{20}{\sqrt{3}}\right)<16$
$n<\left(\frac{16\sqrt{3}}{20}\right)\Rightarrow n<1.38$
$\therefore n=1$