Question

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

Answer 1

Hint: This problem can be solved by realizing the fact that for a normal eye, the far point is at infinity and hence, the corrective lens must diverge the rays coming from infinity such that they are focused at the far point of the defected eye and hence, act as an object for the eye which it can converge on the retina properly.
Formula used:
$P=\dfrac{1}{f\left( \text{in m} \right)}$

Complete step-by-step solution:
For a myopic eye, the far point becomes less than infinity and hence, the person cannot see far away objects properly. So a concave lens is used which can diverge the rays coming from infinity such that they are focused on the far point of the myopic eye and act as a virtual object for it.
Now, for a concave lens, the rays from infinity have diverged such that they appear to come from the focus of the lens. Therefore, since the corrective lens has to focus rays from infinity on to the far point of the myopic eye, the focal length of the lens must be equal to the far point of the myopic eye.
Therefore the focal length of the corrective lens is $f=-40cm=-0.4m$ $\left( \because 1cm=0.01m \right)$
The negative sign is because the focal length of a concave lens is negative according to sign convention.
Now, the power $P$ of a lens of focal length $f$ is given as
$P=\dfrac{1}{f\left( \text{in m} \right)}$ --(1)
Now, using (1), we get the power $P$ of the lens as
$P=\dfrac{1}{-0.4}=-2.5D$
Hence, we have got the focal length and the power of the lens.
Therefore, the correct option is $A)\text{ }-40cm,-2.5D$.

Note: Students must also note that in this problem, for the correction of a myopic eye, a concave lens is used which has a negative focal length as well as a negative power value. Hence, upon careful analysis of the options given, they could right away have inferred that $C)\text{ +}40cm,+2.5D$ and $D)\text{ }-40cm,+2.5D$ are the wrong options and hence, eliminated them. This would have also served as a check for the students to verify whether they have got a wrong answer or not.