Question

Two lenses in contact made of materials with dispersive powers in the ratio`2:1`behaves as ab achromatic lens of focal length `10cm`.The individual focal length of the lenses are :
A. 5 cm, -10cm
B. `-5cm , 10cm`
C. 10 cm, -20 cm
D. `-20 cm, 10 cm`

Answer 1

Correct Answer - B
`(omega_(1))/(f_(1)) + (omega_(2))/(f_(2)) = 0` (condition for achromatism)
`omega_(1) : omega_(2) = 2 :1 ` (Given)
`implies f_(1) : f_(2) = -2 :1` …..(i) ( for fulfills condition)
`(1)/(f_(1)) + (1)/(f_(2)) = (1)/(-10)implies (1)/(f_(1)) (1 + (f_(1))/(f_(2))) = (1)/(-10)` ....(ii)
by (i) & (ii) `f_(1) = 10 cm` & `f_(2) = -5 cm`