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 the reason and also draw a ray diagram for the new position of the object to justify your answer.

Answer 1

1) 40 cm from the mirror

The magnification is given by:

$M=-\frac{q}{p}$

where

q is the distance of the image from the mirror

p is the distance of the object from the mirror

In this problem,

M = -1

q = 40 cm

Therefore, we can find p:

$p=-Mq=-(-1)(40)=40 cm$

2)  At infinite distance

For this part, we need to find the focal length of the mirror first. This can be done by using the mirror equation:

$\frac{1}{f}=\frac{1}{p}+\frac{1}{q}$

where

q = 40 cm is the distance of the image from the mirror

p = 40 cm is the distance of the object from the mirror

f is the focal length

Solving for f,

$\frac{1}{f}=\frac{1}{40}+\frac{1}{40}=\frac{1}{20} \rightarrow f = 20 cm$

Now we can find the new position of the image if the object is moved 20 cm towards the mirror, which means that its new position is

p = 20 cm

Using the lens equation again:

$\frac{1}{q}=\frac{1}{f}-\frac{1}{p}=\frac{1}{20}-\frac{1}{20}=0 \rightarrow q = \infty$

This means that the image is formed at infinity (=is not formed). This can be also seen from the ray diagram attached in the picture.