Final answer:
The power of the convergent and divergent lenses can be found by taking the reciprocals of their focal lengths. The ratio of their dispersive powers is equal to the ratio of their powers. Using this information, the ratio of the dispersive power of the convergent lens to the dispersive power of the divergent lens is 2.5.
Step-by-step explanation:
The power of a lens is defined as the inverse of its focal length. In this case, the achromatic convergent doublet of two lenses in contact has a power of 2D, and the convex lens has a power of 5D. Since power is inversely proportional to focal length, we can calculate the focal lengths of the lenses. The focal length of the convex lens can be found by taking the reciprocal of its power, which is 1/5D or 0.2m. As for the achromatic doublet, we know its power is 2D, so its focal length is 1/2D or 0.5m.
The ratio of the dispersive powers of the convergent and divergent lenses can be found by dividing the dispersive power of the divergent lens by the dispersive power of the convergent lens. The dispersive power of a lens is directly proportional to its focal length, which means it is inversely proportional to its power. Therefore, the ratio of the dispersive power of the convergent lens to the dispersive power of the divergent lens is the same as the ratio of their powers.
Using the calculated focal lengths, the ratio of the dispersive powers is (0.5m)/(0.2m) = 2.5. Therefore, the ratio of the dispersive power of the convergent lens to the dispersive power of the divergent lens is 2.5.