Question

The near point of a longsighted person is 50 cm. Find the power of the convex lens used in his spectacles.

Answer 1

Step 1: Given information,

1. The normal near point for an eye is 25 cm.
2. The distance of the object at the normal near point as per sign convention is $u=-25cm$
3. The distance of the near point for the long-sighted person as per sign convention is $v=-50cm$

Step 2: Calculation of focal length of the convex lens,
Apply the lens formula to calculate the focal length of the lens:

$$\begin{gathered} \frac{1}{f}=\frac{1}{v}-\frac{1}{u} \\ \frac{1}{f}=\frac{1}{-50cm}-\frac{1}{-25cm} \\ \frac{1}{f}=\frac{1}{50} \\ f=50cm \\ f=0.5m \end{gathered}$$

Thus, the focal length of the lens is 0.5 m.

Step 3: Calculation of power of the lens,
Power is defined as the inverse of the focal length of the lens.

$$\begin{gathered} P=\frac{1}{f} \\ P=\frac{1}{0.5m} \\ P=2D \end{gathered}$$

Therefore, the power of the lens is 2D.