Question

The focal length of a convex lens made of flint glass is $15cm$. To remove its chromatic aberration, it is placed in contact with a concave lens made of crown glass. Find the focal length of the concave lens. The ratio of dispersive powers of flint glass to crown glass is $1.5$.

Answer 1

Given: The focal length of a convex lens made of flint glass is 15cm. To remove its chromatic aberration, it is placed in contact with a concave lens made of crown glass. The ratio of dispersive powers of flint glass to crown glass is 1.5.

To find the focal length of the concave lens

Solution:

Let focal length of the convex lens be $f_1$ and focal length of the concave lens be $f_2$ and ratio of dispersice power of the flint glass is $\dfrac {\omega_2}{\omega_1}=1.5$

For achromatic combination,

$\frac{f_1}{f_2}=-\frac{{\omega }_2}{{\omega }_1}⟹\frac{15}{f_2}=-1.5⟹f_2=-10cm$

Hence the focal length of the concave lens is -10cm