Question

(a) Find out the position of the image of an object situated $A$ in the plane mirror (in figure 1).
(b) Can Paheli at $B$ see this image
(c) Can Boojho at $C$ see this image
(d) When Paheli moves from $B{\text{ }}to{\text{ }}C,$where does the image of $A$ move

Answer 1

To solve any problem with light we have to first see the diagram and have to understand the image formation, then we can solve this. Here paheli, Boojho are two-person; we have to change their position to look for the proper answer to the given answer.

Complete step by step answer:
$b$Yes from $B$ can see this image
$c$ yes Boojho can see the image form $C$
let, u be the distance from object
$v$ be the distance from image
$P$ is focal length then,
$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f} = 0$
$\because f = \infty {\text{ }}for{\text{ }}plane{\text{ }}mirror$
$\dfrac{1}{u} = - \dfrac{1}{v}$
Taking derivative in both sides,
$- \dfrac{1}{{{u^2}}}\dot u - \dfrac{1}{{{v^2}}}\dot v = 0 \\\ \dot v = \dfrac{{{v^2}}}{{{u^2}}}\dot u \\\ \dot v = - \dot u \\\$
$\left[ {\because \dfrac{v}{u} = - 1,\dfrac{{{v^2}}}{{{u^2}}} = 1} \right]$
Object is not moving , so the image will be at the same position.
$\therefore$ If Paheli moves from $B$ to $C$ the image will be in the same position.

Note: Always when you are going to observe this problem use diagrams to see the position of the persons. Then you can easily understand the movement of them. By diagram of this question, we can say the following problems. Also here we used the derivatives because here a movement is given to change with a particular distance so we use derivatives.