It is desired to make a converging achromatic combination of mean focal length 50 cm by using two lenses of materials A and B. If the dispersive power of A and B are in ratio 1:2, the focal lengths of the convex and the concave lenses are respectively

Options

A. 25 cm and 50cm
B. 50 cm and 25 cm
C. 50cm and 100 cm
D. 100 cm and 50 cm

Answer

A

Explanation

Ratio of dispersive powers of the lenses, `(omega_(1))/(omega_(2))=1/2`
Now `(f_(1))/(f_(2))=-(omega_(1))/(omega_(2))=-1/2`
or `f_(2)=-2f_(1)`
Now from equivalent focal length
`1/(f_(eq))=1/(f_(1))+1/(f_(2))`
`1/50=1/(f_(1))+1/(-2f_(1))`
or `50f=(-2+1)/(-2f_(1))=1/(2f_(1))`
or `2f_(1)=50 "or" f_(1)=25cm`
Again `f_(2)=-2xx25cm`
`f_(2)=-50cm`