UPSC NDA I 2017 General Ability Solved Paper

Concept:The power of a lens is the reciprocal of its focal length in metres.The lens maker's formula relates the focal length to the radii of curvature and the refractive index.Explanation:Step 1: Convert the given radii from centimetres to metres.For a double convex lens, by sign convention, the first surface is convex ($R_1 = +10\ \text{cm} = +0.1\ \text{m}$).The second surface is concave ($R_2 = -20\ \text{cm} = -0.2\ \text{m}$).Step 2: Apply the lens maker's formula:$\frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$Step 3: Substitute the values: refractive index $\mu = 1.5$, $R_1 = 0.1\ \text{m}$, $R_2 = -0.2\ \text{m}$.$\frac{1}{f} = (1.5 - 1) \left( \frac{1}{0.1} - \frac{1}{-0.2} \right)$$\frac{1}{f} = 0.5 \times (10 + 5)$$\frac{1}{f} = 0.5 \times 15 = 7.5\ \text{m}^{-1}$Step 4: The power $P$ of the lens is given by $P = \frac{1}{f}$.Thus, $P = +7.5\ \text{D}$ (positive sign indicates a converging lens).Answer:$+7.5\ \text{D}$, which corresponds to option A.