Week 12: Lenses and Mirrors 391
Problem 10.α
δ
n
n=1 (air)
light
angle of deviation
apex angle
In the figure above, a beam of light is incident from air onto a prism withanapex angle
α. Its angle of incidence is adjusted until it refractssymmetricallyacross the prism,
with the ray crossing the vertical bisector of the prism at right angles. Prove that the
angle of deviation,δ, is related toαandnby:sin{(α+δ)/ 2 }=nsin(α/2)Advanced Problem 11.n
n=1 (air)
δ angle of deviation
α
apex angle
light
Prove that theangle of deviation,δ, is aminimumwhen the light ray crosses the
vertical bisector at right angles so that the figure has full reflection symmetry if one
reverses the direction of the ray.