Question

The magnification produced by a plane mirror is $+1$. What does this mean?

Answer 1

Hint: Magnification of any mirror can be given by the formula, $m={\displaystyle \frac{v}{u}}$, and for plane mirror it is 1, so using the formula of magnification we will find what is the meaning of magnification $+1$ for a plane mirror.

Formula used: $m={\displaystyle \frac{v}{u}}$

Complete step-by-step solution -
We are given that the magnification of the plane mirror is $+1$ and we are asked to find the reason for it, so, first of all we will understand what magnification is.
“Ratio of image distance to object distance is called magnification.” Which can be give mathematically as,
$m={\displaystyle \frac{v}{u}}$
Where, v is image distance and u is object distance.
Now, in question we are given that value of magnification for plane mirror is $+1$, so on substituting this value in expression we will get,
$1={\displaystyle \frac{v}{u}}$
$v=u$
From the expression derived we can say that for a plane mirror image distance is equal to the object distance. Which means if a person is standing at a distance of $10cm$ from the plane mirror then his image will also be at distance of $10cm$ inside the mirror.
This can be seen in the figure below,

From the figure also it can be said that for a plane mirror, object distance and image distance is equal.

Note: In this we considered the relation of magnification with image and object distance, but students can also consider the relation between height of object and image which can be given as, $$m={\displaystyle \frac{h_i}{h_o}}\Rightarrow 1={\displaystyle \frac{h_i}{h_o}}\Rightarrow h_i=h_o$$ and solve the problem. So this can be considered as an alternate method for solving the problem.