The focal length of 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 = - 50 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) = 6`