The focal length of field achromatic combination of a telescope is `90 cm` .The dispersive powers of lenses are `0.024` and `0.036` respectively .Their focal lengths will be-

Options

A. `30 cm and 60 cm`
B. `30 cm and -45 cm`
C. `45 cm and 90 cm`
D. `15 cm and 45 cm`

Answer

B

Explanation

For achromatic combination
`(f_(1))/(f_(2))=-(omega_(2))/(omega_(1))=-(0.036)/(0.024)=-(3)/(2)`
and `(1)/(f_(1))-(1)/(f_(2))=(1)/(90)`
Solving above equations we get `f_(1)=30cm, f_(2)=-45cm`