Question

A man standing in front of a plane mirror finds his image at a distance of 20 m
from himself. What is the distance of the man from the mirror?

Answer 1

Answer: The distance is 3 metre

Explanation:Hope it helps

Answer 2

Explanation :

Given :

Distance of image of man from himself is 20 m.

Let 'u' be the distance of man from the plane mirror,

and 'v' be the distance of image from plane mirror.

It is given that, V + u = 20m so, V = 20 - u.

Assumption :

Man is standing on left side of plane mirror and let the left side distance be negative (-).. as same right side distance is taken as a positive (+).

Using Mirror formula,

$\frac{1}{u} + \frac{1}{v} = \frac{1}{f} \: \: \: \: (f \: is \: the \: focal \: length)$

Radius of curvature is infinite for plane mirror and that's why focal length (f) is also infinite.

$\frac{1}{ - u} + \frac{1}{20 - u} = \frac{1}{ \infty } \\ \frac{1}{u} = \frac{1}{20 - u} ..(by \: cross \: multiplication) \\ u = 10 \: m.$

The Man is standing at a distance of 10m from plane mirror.