The focal length of a thin biconvex lens is `20 cm`. When an object is moved from a distance of `25 cm` in front of it to `50 cm`, the magni-fication of its image changes from `m_(25) to m_(50)`. The ratio `(m_(25))/(m_(50))` is.

Options

A. 4
B. 6
C. 1
D. 3

Answer

B

Explanation

Case(i), `u = -25 cm, f = 20 cm , v = ?`
`(1)/(f)=-(1)/(u)+(1)/(v) :. (1)/(20)= -(1)/(-25) + (1)/(v)`
or `(1)/(v)=(1)/(20)-(1)/(25)=(1)/(100)` or `v = 100 cm`
`m_(25) = -(v)/(u) = (-100)/(-25) = 4`
Case (ii), `u = -5 cm , f = 20 cm, v = ?`
`(1)/(20)=(-1)/(-50)+(1)/(v)`
or `(1)/(v)=(1)/(20)-(1)/(50) = (3)/(100)`
or `v = (100)/(3) cm`
`m_(50) = (-(100//3))/(-50) = (2)/(3)`
`(m_(25))/(m_(50)) = (4)/(2//3) = (2)/(3)`
`(m_(25))/(m_(50)) = (4)/(2//3) = 6`.