The dispersive powers of the materials of two lenses forming an achromatic combination are in the ratio of `4:3`. Effective focal length of the two lenses is + 60 cm then the focal lengths of the lenses should be

Options

A. -20 cm, 25 cm
B. 20 cm,- 25 cm
C. -15 cm, 20 cm
D. 15 cm,- 20 cm

Answer

D

Explanation

The focal length of the lenses is given,
`1/f = 1/f_(1) + 1/f_(2)`
` implies 1/60 = 1/f_(1) + 1/f_(2)`
`implies1/60= (f_(2)+f_(1))/(f_(1)f_(2))`
`implies1/60= ((-4/3) f_(2)+f_(2))/((-4/3)f_(2)f_(2))`
`implies 1/60 = ((-1)/3)/(-4/3 f_(2))`
`implies f_(2)=15cm`
`f_(1)= (-4)/3 xx15= -20cm`