Show that the angle of deviation of a ray of light on a plane surface is twice the glancing angle

Show that the angle of deviation of a ray of light on a plane surface is twice the glancing angle.

Let g be the glancing angle made by the ray AO with the mirror M1M as shown

d = ZOB = Angle ZOY + angle YOB

angle ZOY = g (opposite angles)

d = g + YOB

but d = g + (90-r)

but r = i (laws of reflection)

therefore, d = (90 – i)

d = g + g (since g = 90 –i)

d = 2g