Shown in the figure are two plane mirrors XY and YZ (XY ⊥ YZ) joined at their edge. Also shown is a light ray falling on one of the mirrors and reflected back parallel to its original path as a result of this arrangement. The two mirrors are now rotated by an angle θ to their new position X′YZ′, as shown. As a result the new reflected ray is at an angle α from the original reflected ray. Then:
- (a)α = 0
- (b)α = θ
- (c)α = 2θ
- (d)α = 4θ
Correct — A, α = 0. Two plane mirrors joined at right angles (XY ⊥ YZ) form a corner reflector. For two mirrors inclined at an angle φ, a ray reflected off both is deviated by 360° − 2φ; with φ = 90° that deviation is exactly 180°, so the emergent ray is antiparallel to the incident ray. Crucially, this deviation depends only on the angle between the mirrors, not on the orientation of the assembly or the angle of incidence. Rotating both mirrors together by θ keeps them perpendicular, so the ray is still sent back antiparallel to the same incident ray — the reflected ray's direction is unchanged. Hence α = 0.
- (b)α = θ — The reflected ray does not simply follow the mirror rotation; the right-angle pair cancels the effect of rotation, so the outgoing direction stays fixed rather than turning by θ.
- (c)α = 2θ — α = 2θ is the result for a single plane mirror (rotating one mirror by θ turns its reflected ray by 2θ). A perpendicular pair of mirrors cancels this doubling, so it does not apply here.
- (d)α = 4θ — There is no mechanism that quadruples the rotation; this over-counts the effect. The corner-reflector geometry keeps the emergent ray fixed, giving α = 0.
When light reflects off two plane mirrors set at an angle φ, the total deviation of the ray is 360° − 2φ, a value fixed by φ alone. A right-angle pair (φ = 90°) therefore always returns the ray with a 180° deviation — antiparallel to the incident ray. This is the principle of the retroreflector (corner reflector) used in bicycle reflectors and lunar laser-ranging reflectors.
The single-mirror rule ('turn a mirror by θ and the reflected ray turns by 2θ') tempts you toward 2θ. But with two perpendicular mirrors the emergent direction is locked to the incident direction independent of orientation, so rotating the pair changes nothing — the answer is 0, not 2θ. The stated perpendicularity is all you need to reason this out.
- Deviation after reflection off two mirrors inclined at φ is 360° − 2φ.
- For φ = 90°, the deviation is 180°, so the emergent ray is antiparallel to the incident ray.
- This deviation is independent of the angle of incidence and of the assembly's orientation.
- Such a right-angle pair is a retroreflector — it sends light straight back regardless of how it is turned.
- Applying the single-mirror '2θ' rule to a two-mirror system.
- Assuming the returned ray must follow the mirrors when they rotate — the corner reflector locks the direction.
Asked as a conceptual optics item testing the fixed-direction property of a right-angle mirror pair.
No directly related past PYQ was found.
- practice — not a real PYQ
Two plane mirrors are inclined at 90°. A ray reflected off both mirrors emerges:
- (a)along the incident ray's path but antiparallel to it
- (b)perpendicular to the incident ray
- (c)at 45° to the incident ray
- (d)in a direction depending on the angle of incidence
Answer(a) antiparallel to the incident ray — the retroreflector property.
- practice — not a real PYQ
If a single plane mirror is rotated by an angle θ while the incident ray is fixed, the reflected ray rotates by:
- (a)0
- (b)θ
- (c)2θ
- (d)4θ
Answer(c) 2θ — the standard single-mirror rotation rule.