Two plane mirrors are inclined to each other at angle θ. A ray of lig…

A ray AB is incident on mirror $OM_1$ at angle $α$ and is reflected along BC suffering a deviation

$δ_1 = ∠FBC$

The ray BC falls on mirror $OM_2$ at an angle of incidence $β$ and is reflected along CD suffering another deviation

$δ_2 = ∠GCD$

The total deviation is $δ= δ_1 + δ_2$

It is clear from the diagram that

$δ_1 = 180° - 2α$ and $δ_2 = 180° - 2β$

$∴ δ = δ_1 + δ_2 = 360° –2(α + β)$

Now, in triangle OBC, $∠OBC + ∠BCO + ∠BOC = 180°$

or $(90° – α) + (90° – β) + θ = 180°$

or $α + β = θ$

Hence $δ = 360° – 2θ$

Which is independent of the angle of incidence $α$ at the first mirror.