Question 54

A biconvex lens of focal length $$20\text{ cm}$$ has curved surfaces whose radii are in the ratio $$1 \colon 2$$. Refractive index of the material of the lens is 1.5. Smaller of the radii of curvatures is

Solution

Let the radii be $$R$$ and $$2R$$. By the lens maker's formula for a biconvex lens, $$\frac{1}{f} = (\mu - 1)\left(\frac{1}{R} + \frac{1}{2R}\right)$$, so $$\frac{1}{20} = 0.5 \times \frac{3}{2R} = \frac{3}{4R}$$. Hence $$R = 15\text{ cm}$$.

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