An achromatic 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 lengths must be respectively

Options

A. `f_(1)=10cms, f_(2)=-20cms`
B. `f_(1)=20cms, f_(2)=10cms`
C. `f_(1)=-10cms, f_(2)=-20cms`
D. `f_(1)=20cms, f_(2)=-20cms`

Answer

A

Explanation

`(f_(1))/(f_(2))=-(omega_(1))/(omega_(2))=-(1)/(2)" "therefore f_(2)=-2f_(1)`
As `(1)/(F )=(1)/(f_(1))+(1)/(f_(2))`
`therefore(1)/(20)=(1)/(f_(1))-(1)/(2f_(1))=(1)/(2f_(1))" "therefore f_(1)=10cm`
`f_(2)=-20cm`