Question

A lens forms a real image 3 cm high of an object 1 cm high. If the separation of object and image is 15 cm, find the focal length of the lens.

Answer 1

Given,
Height of image (​h') = - 3 cm (negative because image is real)
Height of ​object = 1 cm 
Let us first define the sign convention: 
Since the object distance is always negative, let it be -u.
Since the focal length is positive for a convex lens, let it be +f . 

Magnification  =`h/h=v/u` 

`v/u=-3` 

(i) Since object distance (u) is always negative, and the ratio `v/u` here is negative,  v must be positive, i.e., it is on the right side of the lens. 

Now, we have object distance + image distance = 15  

`v+(-u)=15 (using sign convention)`  

`-3u-u=15` 

`-4u=15` 

`u=(-15)/4` 

Applying the lens formula: 

`1/f=1/v-1/u` 

`1/f=1/(-3u)-1/u` 

`1/f=(-4)/(3u)` 

`f=(3u)/-4=(3xx-15/4)/4=45/16=2.81`cm 

Hence, the focal length of the lens is +2.81 cm.