Vijay is unable to focus on objects closer than 2.5 m from his eyes. Approximately what refractive power should his corrective lens have?

Question

Accepted Answer

To determine the refractive power of the corrective lens needed for Vijay, we need to understand the concept of refractive power and how it relates to vision correction.

1. **Explanation for Option 2 (3.6 D):**

Vijay is unable to focus on objects closer than 2.5 meters. This indicates that his near point, the closest distance at which he can see clearly, is 2.5 meters. For normal vision, the near point is typically around 25 centimeters (0.25 meters). To correct his vision, we need to bring his near point from 2.5 meters to 0.25 meters.

The formula for calculating the refractive power $ P $ of a lens in diopters (D) is given by:

$$
   P = \frac{1}{f}
   $$

where $ f $ is the focal length in meters. For corrective lenses, the focal length is related to the desired near point distance. We want Vijay to be able to focus at 0.25 meters, so:

$$
   P = \frac{1}{0.25} - \frac{1}{2.5}
   $$

$$
   P = 4 - 0.4 = 3.6 \, \text{D}
   $$

Therefore, the refractive power required for Vijay's corrective lens is 3.6 D, which corresponds to Option 2.

2. **Explanation for why other options are incorrect:**

- **Option 1 (2.8 D):** This refractive power is too low to correct Vijay's vision from a near point of 2.5 meters to the desired 0.25 meters. Using the formula, a power of 2.8 D would not sufficiently adjust his near point to the standard 0.25 meters.

- **Option 3 (3.2 D):** Similar to Option 1, a refractive power of 3.2 D is insufficient to bring Vijay's near point from 2.5 meters to 0.25 meters. The calculation shows that 3.6 D is needed for this adjustment.

- **Option 4 (2.5 D):** This option is even lower than Option 1 and would not provide the necessary correction for Vijay's vision. It would not bring his near point close enough to the desired 0.25 meters.

In conclusion, Option 2 (3.6 D) is the correct choice because it provides the necessary refractive power to adjust Vijay's near point from 2.5 meters to the standard 0.25 meters, allowing him to focus on objects at a normal reading distance.