An achromatic convergent lens of focal length `150 cm` is made by combining flint and crown glass lenses. Calculate the focal length of both the lenses and point out which one is divergent if the ratio of the dispersive power of flint and crown glasses is `3:2.`

Answer

A, C, D

Explanation

`(omega_1)/(f_1)+(omega_2)/(f_2)=0`
`:. |omega_1/omega_2|=|(f_1)/(f_2)|`
Let 1-stands for flint glass and 2-stands for crown
glass. Then,
`|(f_1)/(f_2)|=3/2 or |f_1|=1.5|f_2|`
Focal length of flint glass is more. So, its power is
less. Combined focal length (and hence combined power)
is positive. So, convex lens (converging
lens) should be made up of crown glass (having
more positive power).
Now, `1/F=1/(f_1)+1/(f_2)`
`:. 1/150=1/(-1.5f)+1/f`
Solving this equation, we get
`f_2=f=50 cm` and
`f_1=-1.5,f=-75 cm`