question_answer

Two plane mirrors \[{{M}_{1}}\] and \[{{M}_{2}}\] each have length 2 m and are separated from one another by 1 cm. A ray of light is incident at one end of mirror \[{{M}_{1}}\] at angle\[45{}^\circ \]. How many reflections the ray will Suffer before going out from the other end? :

A) 100

B) 200

C) 101      

D) 201

Correct Answer: D

Solution :

distance occupied in one reflection,

\[x=\frac{1}{\sin 45{}^\circ }=2cm\]

So total number of reflections on\[{{M}_{2}}\],

\[\frac{200}{2}=100\]

Total number of reflection on \[{{M}_{1}}=101.\]

\[\therefore \]\[N=100+101=201.\]