Question

A person can clearly see objects lying between 25 cm and 2 m from his eye. His vision can be corrected using spectacles of power –
\[\begin{align}
  & \text{A) +0}\text{.25D} \\
 & \text{B) +0}\text{.50D} \\
 & \text{C) -0}\text{.25D} \\
 & \text{D) -0}\text{.50D} \\
\end{align}\]

Answer 1

Hint: We need to understand the power of a healthy human eye to distinguish between the two main eye defects of the human eye. A healthy human eye is entitled to proper vision from 25 cm to infinite distance. We can solve using this data.

Complete step-by-step solution
We are given a condition of the human eye in which the person can see objects from 25 cm to 2 m very clearly. We already know that there are mainly two kinds of eye defects – Myopia or short-sightedness and Hypermetropia or long-sightedness.
Myopia: This eye condition results in the inability to see far away objects clearly. The near objects at the least distance of distinct vision will be perfectly visible, but the vision becomes blurry as the object moves away. This defect is due to the focussing of the image at a point before the retina as seen in the figure.

We can rectify this using a concave lens of suitable focal length or power. In the situation given to us. The person can see objects from 25 cm to 2 m properly. i.e., he is suffering from Myopia. His maximum vision has reduced from infinity to just 2 m.
We can apply the lens formula to find the focal length of the required glass to have the image at infinite distance as –
\[\begin{align}
  & \dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u} \\
 & \Rightarrow \dfrac{1}{f}=\dfrac{1}{\infty }-\dfrac{1}{-2m} \\
 & \therefore f=+2m \\
\end{align}\]
Now, we know that the power of a lens is defined as the inverse of the focal length in meters. So, the power of the lens required to rectify the eye defect is given as –
\[\begin{align}
  & P=\dfrac{1}{f} \\
 & \Rightarrow P=\dfrac{1}{2m} \\
 & \therefore P=+0.50D \\
\end{align}\]
The person needs a +0.50D lens to rectify his vision.
The correct answer is option B.

Note: In this situation, we haven’t considered the 25 cm as a defect. It is because the least distance of distinct vision is 25 cm. Lesser than 25 cm the human eye finds it highly irritating and the strain can cause eye defects if one continues to read for a prolonged time.