Question

A man 160cm high stands in front of a plane mirror. His eyes are at a height 150 cm from the floor. Then the minimum length of the plane mirror for him to see full length image is:
$
  {\text{A}}{\text{. 85 cm}} \\
  {\text{B}}{\text{. 170 cm}} \\
  {\text{C}}{\text{. 80 cm}} \\
  {\text{D}}{\text{. 340 cm}} \\
$

Answer 1

Hint: In this question first we need to know the concept of image formation of a body in a mirror and the case in which the body will see his full image. And then calculate the length of the plane mirror for the body to see his full image using a formed case.

Complete Step-by-Step solution:
It does not matter how far the object is from the mirror. To see a person's full face, the minimum mirror size should be one half the height of the object. It is so since the angle of incidence in reflection is equal to the angle of reflection.
We have,
Height of man= 160cm
His eyes are at a height 150 cm from the floor.
Since, for getting a full image, the length of the mirror should be half that of an object.
 Then,
Length of mirror= $\dfrac{{160}}{2}{\text{cm}}$
                          = 80 cm
Hence, option C. is correct.

Note: Whenever you get this type of question the key concept to solve is to learn image formation of a body in a mirror in different cases. And one more thing to be noted is that the image is a point where the light rays coming from an object meet or appear to meet after reflection or refraction.