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

The achromatic combination from the two lenses is given
`omega_(1)/ omega_(2)=(-f_(1))/f_(2)`
`implies f_(1)=(-omega_(1) f_(2))/w_(2)`
`therefore f_(1)=(-0.45 xx 84)/0.21 =-180cm`