The power of a biconvex lens is 10 dioptre and the radius of curvature of each surface is 10 cm. The refractiv

Question

The power of a biconvex lens is 10 dioptre and the radius of curvature of each surface is 10 cm. The refractive index of the material of the lens is:

Accepted Answer

1. **Identify Given Data:** 
   - Power of the lens, $P = +10 	ext{ D}$ (converging lens).
   - Radius of curvature, $R = 10 	ext{ cm} = 0.1 	ext{ m}$.
   - For a biconvex lens, using the sign convention: $R_1 = +R$ and $R_2 = -R$.
2. **Lens Maker's Formula:** 
   The power of a lens is given by:
   $$ P = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} ight) $$
3. **Calculation:** 
   Substituting the values into the formula:
   $$ 10 = (\mu - 1) \left( \frac{1}{0.1} - \frac{1}{-0.1} ight) $$
   $$ 10 = (\mu - 1) \left( \frac{1}{0.1} + \frac{1}{0.1} ight) $$
   $$ 10 = (\mu - 1) \left( \frac{2}{0.1} ight) $$
   $$ 10 = (\mu - 1) (20) $$
   $$ \mu - 1 = \frac{10}{20} = 0.5 $$
   $$ \mu = 1 + 0.5 = 1.5 = \frac{3}{2} $$
4. **Conclusion:** The refractive index of the material is 1.5 or 3/2.

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