Question

The image of an object formed by a mirror is real, inverted and is of magnification -1. If the image is at a distance of 40 cm from the mirror, where is the object placed ? Where would the image be if the object is moved 20 cm towards the mirror ? State reason and also draw ray diagram for the new position of the object to justify your answer.

Answer 1

Step 1: Given

Magnification, $m=-1$

Image is real and inverted.

So, mirror is concave.

Image distance, $v=40cm$

Object distance, $u$

Step 2: Formula used

magnification, $m=-\frac{v}{u}$

Mirror Formula

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

Step 3: Calculation of object distance

From magnification

$m=-\frac{v}{u}$

$-1=-\frac{(-40)}{u}$

$u=-40cm$

Hence the object is placed at 40 cm from the mirror.

According to the question, magnification is -1. It means that the distance of the image from the mirror is the same as the distance of the object from the mirror and it happens only when the object is placed at the center of the curvature of the mirror.

$\therefore$ Radius of curvature, $R=40cm$

$\therefore$ Focal length, $f=20cm$

Step 4: Finding the image distance for object placed at $20cm$

If the object is moved 20 cm towards the mirror, then its new position would be at the focus of the mirror.
$\therefore$ Position of the image will be at infinity.