Question

Two parallel plane mirrors A and B are placed at a separation 10 cm as shown in figure. A ray incident on the corner of mirror B at an angle of incidence 45 Find the number of times this rays is reflected from mirror A :

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Answer 1

The correct option is B $5$

At mirror B $\angle i=\angle r={45}^0$

At mirror A $\angle i=\angle r={45}^0$by geometry(alternate interior angle,considering both normal parallel lines)

Considering a triangle given in the figure.which is isosceles at mirror A

$\angle i+\angle r={45}^0+{45}^0={90}^0$ and other two are ${45}^0$ each.
Let $x$$=$half of the base of triangle,and h$=$height of the triangle.
$tan\angle i=\frac{x}{h}$

$tan{45}^0=\frac{x}{10};tan{45}^0=1$

$x=10cm$

$2x$$=2\times 10=20=$length of base,it means this rays will get reflected from mirror A at a distance of $20cm$.

The total length of given mirror is $100cm$.So the no. of time rays will reflected from mirror A is $\frac{100}{20}=$$5$.