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Question

Find the angle by which the mirror must be rotated such that the reflected ray will be travelling along the vertical (dotted line) as shown in the figure.
[CW - clockwise, CCW - counter-clockwise]


A
105 CCW
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B
75 CCW
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C
210 CW
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D
15CCW
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Solution

The correct option is D 15CCW
When the plane mirror is not rotated, the reflected ray makes an angle of 30 with the normal, as shown in the figure below.



So, for the reflected ray to become vertical.

Case -I:

Angle by which the reflected ray must be rotated be θ=30CCW.

So,

Angle by which mirror must be rotated be ϕ=θ2=302=15CCW.

Case -II :

Angle by which the reflected ray must be rotated be θ=210CCW

So,

Angle by which mirror must be rotated be ϕ=θ2=2102=105CCW.

Case-III:

Angle by which the reflected ray must be rotated be θ=150CW

So,

Angle by which mirror must be rotated be ϕ=θ2=1502=75CW.

Case -IV:

Angle by which the reflected ray must be rotated be θ=330CW

So,

Angle by which mirror must be rotated be ϕ=θ2=3002=165CW.

These are the four cases by which the reflected will be along the vertical.

It is clear that, Case -I and Case -II are valid and Case- III and Case- IV are invalid for a reason that, a mirror can have only one reflecting surface and the other side is coated.

Hence, options (a) and (c) are correct.

Why this Question?This question provides student a conceptual clarity of rotation of mirror, incident & reflected ray.Note-1 :- The angle turned by the reflected ray is twice the angle turned by the mirror.Note-2 :- If mirror rotates clockwise, then reflected ray will rotate clockwiseExtra credit :- If the mirror is kept fixed and the incident ray is rotated,then the reflected raywill rotate in opposite sense by same angle.

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