Question

A narrow beam of light after reflection by a plane mirror falls on a scale of 100 cm from the mirror. When the mirror is rotated a little the spot moves through 2 cm, find the angle, through which the mirror is rotated.
A- 0.02 rad
B- 0.01 rad
C- 200 rad
D- 0.1 rad

Answer 1

Hint: Images which are real are formed by real meeting of light rays. Plane mirror always forms virtual images and in case of concave it forms both real and virtual images. Reflection of light is the phenomenon in which the beam of light is bounced back into the same medium. There is no change of medium and thus the speed remains the same.

Step by step answer:
We know from the formula, \[\theta =\dfrac{l}{r}\], here l is the length of the arc and r is the radius. This is the angle through the reflected ray which is now being rotated.
We know for the angle of reflection is twice the angle through which the mirror has been rotated. So,
\[\theta =\dfrac{0.02}{2}=0.01\]rad

Thus, the correct option is (B).

Additional information: The angle can be measured either in radians or in degree. Degree is the most commonly used unit of angle measurement.

Note: It is possible that we can have a look at the mirror by holding it in our hands, we could have easily recognized which kind of mirror it is. Because the plane mirror is perfectly flat, the concave mirror is curved and bulged in while the convex mirror is curved and bulged out.