Question

A man is 180 cm tall and his eyes are 10 cm below the top of his head. In order to see his entire height right from the toe to head, he used a plane mirror kept at a distance of 1 m from him. The minimum length of the plane mirror required is
(A) 180 cm
(B) 90 cm
(C) 85 cm
(D) 170 cm

Answer 1

Hint: Examine the factors on which the length of the mirror is concerned. The length of the mirror should be equal to half the height of the object. Explain what should be the position of the plane mirror in front of the object to see its full image.

Formula used:
The length of a mirror,
\[l = \dfrac{h}{2}\]
Here, h is the height of the object.

Complete step by step answer:
We have given the height of the man which is 180 cm and the mirror is placed 1 m away from him.First, we need to understand the conditions that should be fulfilled by the plane mirror in order to show the observer his full image.The length of the mirror does not depend upon the location of our eyes from the top of the head. Also, the distance of the mirror does not affect the image.To see the full image of the man in the plane mirror, the only condition is the mirror length should be half the height of the man.
Therefore,
\[l = \dfrac{h}{2}\]
Here, h is the height of the man.
Substituting 180 cm for h in the above equation, we get,
\[l = \dfrac{{180}}{2}\]
\[ \therefore l = 90\,cm\]

Therefore, the length of the plane mirror should be 90 cm.So, the correct answer is option (B).

Note:We see that the length of the mirror does not depend upon the position of the eyes from the top of the head. However, to see the full image, the mirror should be placed such that, the distance of the eyes from the top of the head in the plane mirror should be half the distance between the eyes and the top of the head. That is, if h is the height of the man, \[{h_1}\] is the distance between the eyes and the top of the head and \[{h_2}\] is the distance between the eyes and the toes, then \[h = {h_1} + {h_2}\].