An achromaic convergent system of focal length `+20cm` is made of two lenses (in contact) of materials having dispersive powers in the ratio `1:2`.Their focal lenths must be respectively

Options

A. `10cm, -20cm`
B. `20cm,10cm`
C. `-10cm,-20cm`
D. `20cm,-10cm`

Answer

A

Explanation

`(omega_(1))/(f_(1)) +(omega_(2))/(f_(2)) = 0 rArr (omega)/(f_(1)) +(2omega)/(f_(2)) = 0`
`f_(2) =- 2f_(1)`
`(1)/(f_(1)) +(1)/(f_(2)) = (1)/(F) rArr (1)/(f_(1))-(1)/(2f_(1)) = (1)/(20)`
`(1)/(2f_(1)) = (1)/(20) rArr f_(1) = 10cm, f_(2) =- 20cm`