Question

A mirror is inclined at an angle of $\theta$ with the horizontal. If a ray of light is incident at an angle $\theta$ with the mirror, then the angle made by reflected ray with the horizontal is:
a. $\theta$
b. $2\theta$
c. $\dfrac{\theta }{2}$
d. zero

Answer 1

As per the property of plane mirror the angle of incidence is equal to the angle of reflection. Angle of reflection, angle of incidence and normal all lie in the same plane. Using this law of plane mirror we will determine the angle made with the horizontal.

Complete step by step answer:
Angle of incidence and angle of reflection are both equal , which is also the property of plane mirrors (used by us in our day to day life, in dressing rooms, in our hand bags etc. Angle of incidence is equal to the angle of refraction condition is fulfilled only when
When both the mediums have the same refractive index.
If the incidence ray falls normally to the surface of the second medium

Magnification produced by the plane mirror is always one.
As the angle of reflection is equal to the angle of incidence theta, therefore angle made by the horizontal and angle of reflection of the mirror are equal. Angles are equal because they are alternate angles and alternate angles are always formed between parallel lines.
Thus, we can say that angle is equal to zero which is made by reflected ray with the horizontal.

Hence, the correct answer is option (D).

Note: Plane mirror has properties like images formed by the plane mirror are upright, left right reversed, virtual and at the same distance as the object is placed away from the mirror. Image forms will be always erect and of the same size as the object used to be.