Question

An object 50 cm tall is placed on the principal axis of a convex lens. Its 20 cm tall image is formed on the screen placed at a distance of 10 cm from the lens. Calculate the focal length of the lens. 

Answer 1

Height of object (h) = 50 cm
Height of image (h') = -20 cm  (real and inverted)
Distance of image from the lens (v) = 10 cm
Distance of object from the lens (u) = ?
Focal length of the lens (f)= ?
We know, magnification (m) of the lens is given by:  

m=`v/u=(h')/h` 

Thus, substituting the values of v, h and h', we get: 

`10/u=(-20)/50 ` 

`10/u=(-20)/50` 

`u=(-5)/2x10` 

∴  u=-25 cm 

Using the lens formula: 

`1/v-1/u=1/f` 

`1/10-1/-25=1/f` 

⇒`1/10+1/25=1/f` 

⇒`(5+2)/5=1/f` 

⇒`7/50=1/f` 

⇒`f=50/7` 

⇒`f=7.14`cm.