Question

A plane mirror is placed 20° above the horizontal on the corner of a room and another plane mirror is placed at the vertical wall. Determine the angle of reflection made by the mirror on the wall.

Answer 1

Answer :

Lets consider that the incident ray is parallel to the horizontal.

The angle of reflection made by the mirror on the wall will be 40^o

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According to the law of reflection. The angle of incidence is always equal to the angle of reflection.

Where, angle of incidence is the angle between the normal to the plane of the mirror and the incident ray.

and, angle of reflection is the angle between the normal to the plane of the mirror and the reflected ray.

Here we have given :

A plane mirror is placed 20^o above the horizontal.

From the given diagram :

θ₁ = 20^o

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From the geometry : θ₂ = θ₁ = 20^o

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Therefore, Angle of incidence for the inclined mirror will be :

θ₃ = 90^o - 20^o = 70^o

And, According to the law of reflection.

Angle of incidence will be always equal to the angle of reflection.

Thus, Angle of reflection for the inclined mirror (θ₄) will be : θ₄ = θ₃ = 70^o

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And, θ₅ = 90^o - θ₄ = 90^o - 70^o = 20^o

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Now from the diagram : θ₁ + θ₆ = 90^o (Sum of the two angles opposite to the right angle)

∴ θ₆ = 90^o - θ₁ = 90^o - 20^o = 70^o

and, θ₇ + θ₆ = 180^o

Thus : θ₇ = 180^o - θ₆ = 180^o - 70^o = 110^o

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Similarly, θ₅ + θ₇ + θ₈ = 180^o (Sum of the interior angles of a triangle is always 180^o)

∴ θ₈ = 180^o - θ₅ - θ₇

∴ θ₈ = 180^o - 20^o - 110^o

∴ θ₈ = 50^o

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Therefore, Angle of incidence for the Vertical mirror will be : θ₉ = 90^o - θ₈ = 90^o - 50^o = 40^o

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Finally,

According to the law of reflection.

Angle of incidence will be always equal to the angle of reflection.

.

Thus, Angle of reflection for the vertical mirror (θ₁₀) will be : θ₁₀ = θ₉ = 40^o