Question

a ray of light falls on a plane mirror. when the mirror is rotated by 20 degrees,the angle between the incident ray and reflected ray is 45 degrees. the original angle between incident ray and reflected ray is ?

Answer 1

A ray of light striking the mirror at an angle of incidence θ is reflected at the same angle.The deviation i.e.,the angle between incident and reflected rays is 180⁰ - 2θ.

Now, if the direction of the incident ray is unchanged and mirror is rotated through an angle Φ.
then each of the angles of incidence and reflection becomes (θ+Φ).The deviation is
( 180 - 2(θ+Φ)).

Given,
Angle between reflected and incident wave when mirror is rotated = 45⁰ .
Angle of rotation i.e. Φ = 20⁰
45⁰= 180⁰-2(θ+20⁰ )
So,original angle between incident and reflected ray is 180⁰ - 2θ= 5⁰