question_answer

Two plane mirrors \[{{M}_{1}}\] and \[{{M}_{2}}\] have a length of 2 m each and are 10 cm apart. A ray of light is incident on one end of mirror \[{{M}_{2}}\] at an angle of 30. The number of reflections light undergoes before reaching the other end is

A)  \[20\sqrt{3}\]    

B)         \[100\]

C)  150                       

D)         200

Correct Answer: A

Solution :

 The distance travelled by the .incident ray along the length of mirror in one reflection is denoted by \[x\] in the given figure.                 \[\tan 30=\frac{x}{10}\] \[\Rightarrow \]               \[x=\frac{10}{\sqrt{3}}cm\]. Now total number of reflections \[\text{=}\frac{\text{total}\,\,\text{distance}\,\,\text{covered}\,\,\text{by}\,\,\text{ray}\,\,\text{along}\,\,\text{the}\,\,\text{length}\,\,\text{of}\,\,\text{mirror}}{\text{distance}\,\,\text{covered}\,\,\text{by}\,\,\text{the}\,\,\text{ray}\,\,\text{in}\,\,\text{one}\,\,\text{reflection}}\]\[=\frac{200}{10\sqrt{3}}=20\sqrt{3}\]