Two plane mirrors are inclined at angle`theta`.A ray of light is incident on one mirror at an angle of incidence.i.The rayis refelected from this mirror,falls on the second mirror from where it is refleced parallel to the first mirror .What is the value of i,the angle of incident in term of `theta`?

Explanation

The situation is illustrated in figures.`XA`is the incident ray.`BC`is the final reflected ray.it is given that `BC`is parallel to mirror`M_(1)`.Look at the assignment of the angles carefully .Now `N_(2)`is normal to mirror`M_(2)`Therefore.
`beta=theta`
Then from`Delta OAB`
`theta+beta+90^(@)-i=180^(@)`
or `theta+theta+90^(@)-i=180^(@)`
or `i=2theta-90^(@)`
Thus if the angle of incidence is `i=2theta-90^(@)`,then the final reflected ray will be parallel to this first mirror.