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.

A
10cm
B
+10cm
C
20cm
D
+20cm
Solution
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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 f1 and focal length of the concave lens be f2 and ratio of dispersice power of the flint glass is $\dfrac {\omega_2}{\omega_1}=1.5$
For achromatic combination,
f1f2=ω2ω115f2=1.5f2=10cm
Hence the focal length of the concave lens is -10cm

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