An achromatic doublet of focal length `90` cm is to be made of two lenses, the material one having `1.5` times the dispersive power of the other. The doublet is converging type. Find the focal length of each of lens.

Explanation

To solve the problem of finding the focal lengths of the two lenses in an achromatic doublet, we can follow these steps:

### Step 1: Understand the relationship between dispersive power and focal lengths
For an achromatic doublet, the relationship between the dispersive powers \( w_1 \) and \( w_2 \) of the two lenses and their focal lengths \( f_1 \) and \( f_2 \) is given by:
\[ \frac{w_1}{w_2} = -\frac{f_1}{f_2} \]

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