Question

When an object is placed 20 cm from a concave mirror, a real image magnified three times is formed. Find:

(a) the focal length of the mirror.
(b) Where must the object be placed to give a virtual images three times the height of the object? 

Answer 1

Given,

Distance of the object 'u' = -20 cm
Magnification 'm' = −3
(a)We have to find the focal length of the mirror.

 Using the magnification formula, we get 

`m=-v/u` 

`-3=(-v)/-20` 

v=-60cm  

Therefore, the distance of the image 'v' is −60 cm.
Using the mirror formula, we get 

`1/f=1/v+1/u` 

`1/f=1/-60+1/-20`  

`1/f=-1/60-1/20` 

`1/f=-1/60-3/60=-4/60` 

`1/f=(-1)/15` 

f=-15 cm 

Thus, the focal length of the concave mirror is 15 cm.

(b) Now, if the image is virtual and 3 times magnified, then we have to find the position of the object.

Given,

Focal length of the concave mirror = −15cm 

Magnification 'm' = 3

Using the magnification formula, we get 

`m=-v/u` 

`3=-v/u` 

`v=-3u` 

Therefore, the distance of the image 'v' is −3u

Again, using the mirror formula, we get  

`1/f=1/v+1/u` 

`1/f=1/(-3u)+3/(3u)=2/(3u)` 

`f=(3u)/2` 

`u=(2f)/3=(2xx(-15))/3` 

`u=-10 cm ` 

Thus, the object should be placed at a distance of 10 cm to get a virtual image three times the height of the object.