An object is placed first at infinity and then at 20 cm from the object side focal plane of a convex lens. The two images thus formed are 5 cm apart the focal length of the lens is

Options

A. 5 cm
B. 15 cm
C. 10 cm
D. 25 cm

Answer

C

Explanation

In the first case, `u_(1)=oo`
`therefore (1)/(v_(1))-(1)/(u)=(1)/(f) therefore (1)/(v) =(1)/(f) or v_(1)=f`
In the second case, `u_(2)=f+20` and u is negative and `v_(2)=f+5`
`therefore (1)/(f+5)+(1)/((f+20))=(1)/(f)`
`therefore (f+20+f+5)/((f+5)(f+20))=(1)/(f)`
`therefore f^(2) +20f+f^(2)+5f=f^(2)+20f+5f+100`
`therefore f^(2)=100 therefore f=10 cm`