## Question

For an achromatic combination of lenses, the ratio of dispersive powers of materials used in lenses is 2:3. One lens has focal length equal to 10 cm. Find focal length, power and nature of second lens.

### Solution

– 15 cm (concave),

The condition for achromatism of two lenses in contact is

In an achromatic (convergent) lens-doublet the dispersive power of the material of the convex lens is less than that of the concave lens. Here, the dispersive powers are in the ratio 2:3. Therefore, the first lens is convex and the second is concave.

If we take the focal length of the first (convex) lens as 10cm, then

From eq. (i), we have

The power of the second lens is

If we take the focal length of the second (concave) lens as 10 cm, then

Power,

#### SIMILAR QUESTIONS

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