Question

Two plane mirrors A and B are aligned parallel to each other as shown in the figure. A light ray is incident at an angle of ${30}^{\circ }$ at point just inside one end of A. The Plane of incidence coincides with the plane of the figure. How many reflections will occur between the mirrors?

• A. 25
• B. 50
• C. 32
• D. 30

Answer 1

The correct option is D 30


$In\Delta ABC\frac{BC}{AB}=tan{30}^{\circ }\frac{x}{0.2}=\frac{1}{\sqrt{3}}x=\frac{0.2}{\sqrt{3}}\text{Let n be the no of reflections between}\text{the mirrors}nx=2\sqrt{3}n\left(\frac{0.2}{\sqrt{3}}\right)=2\sqrt{3}n=\frac{2\sqrt{3}\times \sqrt{3}\times 10}{2}=30\text{Hence, no. of reflections that will}\text{take place between plane mirrors is 30.}$