The focal length of a lens of dispersive power 0.45 which should be placed in contact with a convex lens of focal length 84 cm and dispersive power 0.21 to make the achromatic combination from the two lenses, in cm is

Options

A. 45
B. 90
C. 180
D. `-180`

Answer

D

Explanation

In achromatic combination of lenses, there must be two lenses having focal lengths f and f. and their respective dispersive power `omega` and `omega.`.
`:. (omega)/(f)+(omega.)/(f.)=0`
`omega=0.45, omega.=0.21, f. = +84` (convex lens)
`(0.45)/(f) + (0.21)/(84)=0`
`f= -(0.45xx84)/(0.21)`
`f= -180cm`