In figure, AB is the incident ray. When a ray of light AB strikes in surface DE, then it returns back to BC making angle (r) which is called angle of reflection. Let ABF be the original path of the incident ray. Here δ is the deviation produced by the reflecting surface.
We have to know the definition of few special terms.
Angle of deviation: It is the angle made by the reflected ray and the original path of the incident ray.
In the above given figure, ∠DBA is the angle of deviation.
Glancing angle: It is the angle made by the angle of incident with the refracting surface. In figure ∠ CBF is the glancing angle.
Now, from figure:
∠CBF = ∠CBE + ∠EBF
or, ∠CBF = 90º – r + θ
or, ∠CBF = 90º – i + θ [Since i = r]
or, ∠CBF = θ + θ
∴ ∠CBF = 2θ
This proves that the deviation produced by the mirror is twice the glancing angle.