Question

A converging mirror forms a real image of height 4 cm of an object of height 1 cm placed 20 cm away from the mirror:

1. Calculate the image distance.
2. What is the focal length of the mirror?

Answer 1

A concave mirror is a converging mirror.

Distance of the object from the mirror μ = −20 cm

Height of the object h_o = 1 cm

Height of the image h_i = v4 cm

We have to find the distance of the image v and the focal length of the mirror f.

Using the magnification formula, we get 

`m = h_i/h_o = (-v)/u`

⇒ `(-4)/1 = (-v)/-20`

`v = 20 xx (-4)/1 = -80` cm

Thus, the distance of the image v is 80 cm.

Now, using the mirror formula, we get 

`1/f = 1/v + 1/u` 

`1/f = 1/-80 + 1/-20`

= `-1/80 -4/80`

= `-5/80`  

`1/f  =  -1/16` 

f = −16 cm 

Thus, the focal length of the concave mirror is −16 cm.