A biconvex lens has radii of curvature, 20 cm each. If the refractive index of the material of the lens is 1.5

Question

A biconvex lens has radii of curvature, 20 cm each. If the refractive index of the material of the lens is 1.5, the power of the lens is:

Accepted Answer

1. **Identify Given Data:** 
   - Refractive index, $\mu = 1.5$.
   - Radii of curvature for a biconvex lens: $R_1 = +20 	ext{ cm} = +0.2 	ext{ m}$ and $R_2 = -20 	ext{ cm} = -0.2 	ext{ m}$ (using Cartesian sign convention).
2. **Lens Maker's Formula:** 
   The power ($P$) of a lens is given by:
   $$ P = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} ight) $$
3. **Calculation:** 
   Substituting the values:
   $$ P = (1.5 - 1) \left( \frac{1}{0.2} - \frac{1}{-0.2} ight) $$
   $$ P = 0.5 \left( \frac{1}{0.2} + \frac{1}{0.2} ight) $$
   $$ P = 0.5 \left( \frac{2}{0.2} ight) $$
   $$ P = 0.5 	imes 10 $$
   $$ P = +5 	ext{ D} $$
4. **Conclusion:** The power of the lens is +5 Diopters.

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