It maybe caused in two ways depending on how the incident ray is made to fall on the mirror.
Case-I When the ray is incident at an angle 30∘ above the horizontal.
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Let the angle be θ∘with which the mirror to be placed with the horizontal so as to reflect vertically the ray incident on the mirror at 30∘ with the horizontal.
Incident ray is inclined at angle 30∘ (above) with the horizontal and reflected ray is vertical. So the angle between reflected ray and incident ray may be (90∘−30∘)=60∘ Hence angle of incidence will be =12×60∘=30∘
So it is obvious that
θ+30∘+30∘=90∘
⇒θ=30∘
Case-II When the ray is incident at an angle 30∘ below the horizontal.
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In this case if mirror makes an angle θ to reflect the incident ray in vertical direction, then the vertical reflected ray will make (90−θ)∘ with the mirror.
So the angle of reflection becomes (90∘−(90−θ)∘)=θ∘
But the incident ray makes an angle 30∘ below the horizontal. So it makes an angle (90∘+30∘)=120∘with the vertical reflected ray and as a result the angle of incidence or the angle of reflection becomes 12×120∘=60∘
So we have θ=60∘
