Question

The two lenses of an achromatic doublet should have:
A. Equal powers
B. Equal dispersive powers
C. Equal ratio of their power and dispersive power
D. Sum of the product of their powers and dispersive power equal to zero

Answer 1

Hint: To solve this question we have to know what is lens and the types of lenses. Lens is a piece of glass which is curved and it makes things bigger or smaller, clear etc when we look through it. We have to know that an achromatic doublet is formed by combining two lenses. These achromatic lenses are made for preventing spherical aberration.

Complete answer:
From the hint part we can now tell that to form achromatic doublet two lenses are needed. And two lenses form a pair such that the combination of these do not split into its constituent colour. Like, if we use white light then there is a high chance to break the white light into seven constituent colors.

So, the lenses are paired in a way that will not break any light into its constituent colors. So, we can say that the net dispersive power is zero. From this condition we can say that the two lenses of an achromatic doublet should have sum of the product of their powers and dispersive power equal to zero.

Then the right option would be option D.

Note: We can get confused between the properties of prism and the properties of an achromatic doublet of two lenses. But prism can split lights into their constituent colors. So, we have to know deeply about these lenses and prisms to answer these types of more questions.