Question

Prove that if a ray of light is obliquely incident on one of the two mirrors inclined at an angle theta with each other, the net daviation of ray, after reflection from both the mirrors, is independent of the angle of incidence.

Answer 1

Consider a ray SA getting reflected from A at the first mirror and successively from B at the second mirror. Finally, the ray proceeds towards BI. Let, i₁ and i₂ be the angles of incidences at the two mirrors.

∠BAO = 90° - i₁  &

∠ABO = 90° - i₂

In ΔOAB,

θ + ∠BAO + ∠ABO = 180°

θ + 90° - i₁ + 90° - i₂ = 180°

θ = i₁ + i₂

or,

Deviation at A = π - 2 i₁

Deviation at B = π - 2 i₂

Not deviation δ of the ray is given by,

δ = π - 2 i₁ +π - 2 i₂

   = 2π - 2( i₁ + i₂)

or, δ = 2 (π - θ)

Thus, the deviation only depends upon the angle between the two mirrors. It does not depend upon the angle of incidence.

Answer 2

Answer

Refer the above attachment.