A boy is 1.8 m tall and can see his image in a plane mirror fixed on a wall. His eyes are 1.6 m from the floor level. The minimum length of the mirror is

Question

A boy is 1.8 m tall and can see his image in a plane mirror fixed on a wall. His eyes are 1.6 m from the floor level. The minimum length of the mirror is (A) 0.1 m (B) 0.7 m (C) 0.9 m (D) 0.5 m

Tardigrade Admin · Accepted Answer

As the ray from feet enters the eye after striking the mirror at

M_{2}

, so height of

M_{2}

from ground level is half of the eye level from ground, i.e.,

\frac{1.6}{2} = 0.8 m

.

Similarly, a ray from the head enters the eye after striking the mirror at

M_{1}

, so position of

M_{1}

from the head level is half the distance between head and eye level.
i.e.,

\frac{1.8 - 1.6}{2} = \frac{0.2}{2} = 0.1 m

So, minimum length of mirror is

[1.8 - (0.8 + 0.1)] = 0.9 m

Minimum length of mirror is independent of the eye level because it is equal to the half the height of the boy.

Q. A boy is 1.8 m tall and can see his image in a plane mirror fixed on a wall. His eyes are 1.6 m from the floor level. The minimum length of the mirror is

0.1 m

0.7 m

0.9 m

0.5 m