A student of height 1.9 m can see his full image in a plane mirror fixed on a wall. His eyes are 1.85 m from the floor level. What is the minimum length of the plane mirror required to get the full image of the student ?

Options

A. `0.1` m
B. `0.7` m
C. `0.9` m
D. `0.5` m

Answer

C

Explanation

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 , i.e., `(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., `(1.8-1.6)/(2)=(0.2)/(2)=0.1` m
So, minimum length of mirror is `[1.8-(0.8+0.1)]=0.9` m minimum of length of mirror is independent of the eye level because it is equal to the half the height of the boy.