Question

Two plane mirrors are inclined to each other at a certain angle. a ray of light first incident on a one of them at the at an inclination 10 degree with the mirror retraces its path after five reflections. the angle between the mirror is

Answer 1

Given that,

Two plane mirrors are inclined to each other at a certain angle.

Incident angle = 10°

Let the angle between the mirror is θ.

On second mirror ray of light retraces its path

After five reflection it will be same.

So, ray of light falls normally on the second mirror

The normal angle is

$a=90^{\circ}$

We know that,

From snell's law,

Incident angle is equal to the reflection angle.

$\angle i=\angle r$

We need to calculate the angle b

Using formula for b

$b=90-r$

Put the value into the formula

$b=90-10$

$b=80^{\circ}$

We need to calculate the angle between the mirror

Using formula of angle

$\theta=180-(a+b)$

Put the value into the formula

$\theta=180-(90+80)$

$\theta=180-170$

$\theta=10^{\circ}$

Hence, The angle between the mirror is 10°.