Question

An object of height 4 cm is placed at a distance of 15 cm in front of a concave lens of power, −10 dioptres. Find the size of the image.

Answer 1

Object distance u = -15 cm
Height of object h  = 4 cm
Power of the lens p = -10 dioptres
Height of image h' = ?
Image distance v = ?
Focal length of the lens f = ?  

We know that: 

`p=1/f` 

`f=1/p` 

⇒`f=1/-10` 

⇒ `f=-0.1m =-10 cm` 

From the lens formula, we have: 

`1/v-1/u=1/f` 

`1/v-1/-15=1/-10` 

⇒`1/v+1/15=-1/10` 

⇒`1/v=-1/15-1/10` 

⇒`1/v=(-2-3)/30` 

⇒`1/v=-5/30` 

⇒`1/v=-1/6` 

⇒`v=-6` cm 

Thus, the image will be formed at a distance of 6 cm and in front of the mirror.
Now, magnification m  =`v/u=(h')/h`  

or `(-6)/(-15)=(h')/4` 

`h'=(6x4)/15` 

`h'=24/15` 

∴`h'=1.6 cm`