Question

A man \[1.8\,{\text{m}}\] tall wishes to see a full-length image in a plane mirror. The length of the shortest mirror in which he can see his entire image is:
(Assume that the mirror is hanging vertically on a wall in front of the man).
A. \[0.6\,{\text{m}}\]
B. \[0.9\,{\text{m}}\]
C. \[1.2\,{\text{m}}\]
D. \[1.5\,{\text{m}}\]

Answer 1

Hint: First of all, we analyse the image formation by a plane mirror.
The image is formed behind the mirror in case of a plane mirror and the image is a virtual one.
 It produces an image which is the same size as the object.

Complete step by step answer:
In the given problem, we are supplied with the following data:
The height of the man is \[1.8\,{\text{m}}\] and is standing in front of a plane mirror.
We are asked to find the length of the shortest mirror in which he can see his entire image.
The mirror is hung vertically on a wall in front of him.
At least half as tall as the person standing in front of him must be the mirror. As the individual is 180 cm long, at least 90 cm must be the vertical dimension of the mirror. The lower edge of the mirror must be half the gap between his feet and his eyes in height.
We can explain this fact by simply analysing or going through the laws of reflection.
The incident ray, the reflected ray and the normal to the surface of the mirror, all lie on the same plane.
The incident ray makes an angle with the normal which is called the angle of incidence.
Again, the reflected ray makes an angle with the normal which is called the angle of reflection.
In this case, the angle of incidence is always equal to the angle of reflection.
Consider a case where, as seen in the figure below, a light ray from an object gets reflected by a mirror and enters the eye. If the object and the eye are at the same distance from the mirror, the law of reflection means that precisely halfway between the object and the eye lies the point of incidence.
Since, the height of the man is \[1.8\,{\text{m}}\] .
Hence, the length of the shortest mirror in which the man can see his entire image is:
$= \dfrac{{1.8}}{2}\,{\text{m}} \\
= 0.9\,{\text{m}} \\$

So, the correct answer is “Option B”.

Note:
A plane mirror always produces a virtual image and the size of the image is always equal to the size of the object.
The magnification of the image produced by a plane mirror is always \[1\] .
The image produced by a plane mirror is behind the mirror.