Question

A person needs a lens of power +2 D for correcting his near vision. What is the focal length of the lens?

Answer 1

Step 1: Given data

The required power of the lens is + 2 D.

Step 2: Definition of Hypermetropia (far-sightedness)

1. A person with hypermetropia can see distant objects clearly, but cannot see nearby objects distinctly.
2. The normal eye has a near point of about 25 cm. A person with hypermetropia may have a near point several meters away from the eye.

Step 3: Formula used

Power of the lens, $P=\frac{1}{f(\mathrm{in}\mathrm{meters})}$

Step 4: Calculation of the focal length and nature of the lens

$$\begin{gathered} f(\mathrm{in}\mathrm{meters})=\frac{1}{P} \\ f=\frac{1}{2\mathrm{D}} \\ f=0.5\mathrm{m} \\ f=+50\mathrm{cm} \end{gathered}$$

As the focal length is positive, a convex lens with the focal length of $50\mathrm{cm}$ is required to correct the vision defect of the person.