Question

Two plane mirrors are inclined at an angle `theta` . Light ray is incident parallel to one of the mirror.For what value of `theta`ray will retrace it's path after third reflection. ?

Answer 1

`theta=30^@`

Explanation:

Let MN and MP are two plane mirrors be inclined at an `anglePMN=theta`. A light ray AB parallel to MN is incident on MP and the ray after third reflection on MP at B retraces its path as shown in the diagram. Hence CD is perpendicular to MP.

This means `angle BCN=angle DCM=90^@-theta`.
`AB"||"MN` and BC is the intercept.

So `anglePBA="corresponding "anglePMN=theta`

And `angle ABC=180^@-2theta`

Since `AB"||"MN` and BC is the intercept ,

then

`angle ABC+angleBCN=180^@`

`=>180^@-2theta+90^@-theta=180^@`

`=>3theta=90^@`

`=>theta=90^@/3=30^@`