Two convex lenses of focal lengths `f_(1)` and `f_(2)` form imgaes with magnification `m_(1)` and `m_(2)` when used individually for an object kept at the same distance from the lenses. Them `f_(1)//f_(2)` is

Options

A. `(m_(1)(1 - m_(2)))/(m_(2)(1 - m_(2)))`
B. `(m_(1)(1 - m_(2)))/(m_(2)(1 - m_(1)))`
C. `(m_(2)(1 - m_(1)))/(m_(1)(1 - m_(2)))`
D. `(m_(2)(1 - m_(2)))/(m_(1)(1 - m_(1)))`

Answer

b

Explanation

The linear magnification of lens in terms of focal length f and u
`m = (f )/(f + u)`
For first lens,
`u_(1) = ((1 - m_(1))/(m_(1)))F_(1)`
For second lens
`u_(2) = ((1 - m_(2))/(m_(2))) f_(2)`
According to the question,
`u_(1) = u_(2)`
`:. ((m_(1) - 1))/(m_(1)) f_(1) = ((m_(2) - 1))/(m_(2)) f_(2)`
`(f_(1))/(f_(2)) = (m_(1))/(m_(2)) . ((m_(2) - 1))/((m_(1) - 1))`
`= (m_(1)(m_(2) - 1))/(m_(2)(m_(1) - 1))`