Question

An object is 2 m from a lens which forms an erect image one-fourth (exactly) the size of the object. Determine the focal length of the lens. What type of lens is this?

Answer 1

Given:
Object distance (u) =-2 m
Image distance (v) = ?
Magnification (m) = 0.25 (one-fourth of the size of the image)
Focal length (f) = ?
Magnification (m) =`v/u` 

`0.25=v/-2` 

v=-0.5m 

Putting these values in lens formula, we get: 

`1/v-1/u=1/f` 

`1/-0.5+1/-2=1/f` 

`1/-0.5+1/2=1/f` 

`1/f=1/2-1/0.5` 

`1/f=1/2-10/5` 

`1/f=(-3)/2` 

`f=-0.66` m 

Negative sign of focal length shows that lens is diverging in nature. Hence, it is a concave lens.