Question

If a mirror gets turned through an angle the reflected ray also gets turned through certain angles suppose the plane mirror is turned through 30° prove by using laws of reflection that the reflected ray turns by 60°.

Answer 1

Consider a plane mirror and a fixed incident ray of light reflecting from the surface at an angle θ. Before the mirror has rotated, the angle of incidence is θ as is the angle of reflection.
If the mirror is rotated by an angle of 30^₀, the normal is rotated by an angle of 30^₀; thus, the angle of incidence increases to θ + 30^₀. Therefore, the angle of reflection must also increase by θ to θ + 30^₀ .

Difference between the final angle of reflection and the initial angle of reflection = $2\times 30={60}^{\mathrm{o}}$