A ray of light in the plane of two plane mirrors and first strikes

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Geometric Optics · Geometric Optics

Problem

A ray of light in the plane of two plane mirrors

M_{1}

and

M_{2}

first strikes

M_{1}

, is reflected to

M_{2}

, and then leaves the region after a second reflection. The mirrors intersect at an angle

\phi

. Develop a general proof for the angular relationship between the incident and emergent rays. (i) Let the incident ray make an angle

i

with the normal to

M_{1}

. Using geometrical construction, express the direction of the ray after the first reflection in terms of

i

and

\phi

. (ii) Derive an expression for the angle of incidence on

M_{2}

in terms of

i

and

\phi

. (iii) Hence obtain a simplified expression for the angle

\Delta

between the original incident ray and the final emergent ray, and show explicitly that

\Delta = 2\phi

and is independent of

i