Question

The far point of a myopic person is 40cm. To see the distant objects clearly, the focal length and the power of the lens used should be:
A. -40cm, -2.5D
B. -25cm, -4.0D
C. +40cm, +2.5D
D. -40cm, +2.5D

Answer 1

Hint: For myopic person the far point shifts from infinity to a finite point. So to correct it a lens must be used which can convert the finite point to infinity once again. By using the general lens formula we can find the focal length of the required lens.
As per the information given in the question;
Far point of myopic person (u) is 40 cm.

Complete step-by-step answer:
The general formula for focal length is given by:
${\displaystyle \frac{1}{f}}={\displaystyle \frac{1}{v}}-{\displaystyle \frac{1}{u}}$ ----------(1)
The power of the lens is determined by:
$D={\displaystyle \frac{1}{f_{(inmeters)}}}$ -----------(2)
Step by step solution:
According to the given question the far point of the myopic person is 40cm which must be infinity for a healthy person. So for the correction the of visions lens which will be used have focal length of:
By equation (1)
${\displaystyle \frac{1}{f}}={\displaystyle \frac{1}{v}}-{\displaystyle \frac{1}{u}}$
Final point (v) will be infinity in case of myopic defect and the initial point for this question is at 40cm from the viewer.
$\begin{array}{rl}& {\displaystyle \frac{1}{f}}={\displaystyle \frac{1}{\mathrm{\infty }}}-{\displaystyle \frac{1}{40}}\\ & {\displaystyle \frac{1}{f}}=-{\displaystyle \frac{1}{40}}\\ & f=-40cm\end{array}$
So, the focal length of the lens will be -40cm, which is -0.4m.
From equation (2), the power of the lens will be:
$D={\displaystyle \frac{1}{f_{(inmeters)}}}$
By potting the calculated value of focal length:
$\begin{array}{rl}& D={\displaystyle \frac{1}{-0.4}}\\ & D=-2.5D\end{array}$
The power of the lens will be -2.5D. Minus sign denote that the required lens will be a concave lens
So the correct option which will satisfy the question will be option A.

So, the correct answer is “Option A”.

Note: Use the general formula for focal length to be used with proper sign conventions. The focal length of the lens must be converted into meters before using it for power determination.