Question

A person cannot see distinctly objects kept beyond$2m$. This defect can be corrected by using a lens of power

• A. + 0.5 D
• B. – 0.5 D
• C. + 0.2 D
• D. – 0.2 D

Answer 1

The correct option is B

– 0.5 D

Step (1): Given:

The far point of the person, $D=2m$

This means the person cannot see the objects situated beyond 2 m from the eye.

Step (2): Statement of Myopia:

Short-sightedness is an eye defect that causes the person to see far away objects as blurry or out of focus. The scientific term in use for short-sightedness is myopia.

From the given situation, the person is suffering from short-sightedness (or) myopia. A concave lens is used to correct myopia.

The far point of the given myopic eye, D is at 2 m.

Step (3): Finding the focal length of the lens:

Let the object distance $u=-\infty$and image distance (v) = distance of far point = -D
Let 'f' be the focal length of the bi-concave lens.
Using the lens formula,$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$$\begin{gathered} \frac{1}{f}=\frac{1}{\infty }-\frac{1}{2} \\ \frac{1}{f}=-\frac{1}{2} \\ \therefore f=-2m \end{gathered}$$

Step (4): Finding the power of the lens:

We know that the required power of the lens,

$$\begin{gathered} P=\frac{1}{f} \\ Bysubstitutingthegivenvalue,weget \\ P=\frac{1}{-2} \\ =-0.5D \end{gathered}$$

A concave lens of power of -0.5 D is required to fix the myopic eye.

Hence, the correct answer is (B) – 0.5 D