Suppose that the spotlight shines so that different parts of the beam reflect off of different two surfaces, one inclined at an angle α (from the horizontal) and one inclined at an angle β. What would the angular separation Δθ be between the rays reflected from the two surfaces? Assume that the light comes at an angle θa to the vertical. Express your answer in terms of some or all of the angles θa, α, and β.

Question

Physics

Mira Kerr

9 January, 11:13

Suppose that the spotlight shines so that different parts of the beam reflect off of different two surfaces, one inclined at an angle α (from the horizontal) and one inclined at an angle β. What would the angular separation Δθ be between the rays reflected from the two surfaces? Assume that the light comes at an angle θa to the vertical. Express your answer in terms of some or all of the angles θa, α, and β.

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Answers (1)

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Curtis Wheeler · Answer 1

For reflection from first surface,

angle of incidence = angle of reflection

θa = angle of reflection

Now reflecting surface turns by angle (β - α), so reflected ray will turn by twice the angle. So angle between two reflected rays will be equal to

2 (β - α)

So Δθ = 2 (β - α)

This is the required relation.