Question

A myopic person has been using spectacles of power 1.0 diopter for distant vision. During old age he also needs to use a separate reading glass of power +2.0 diopters. Explain what may have happened.

Answer 1

Use the formula for focal length. This formula gives the relation between the focal length of the lens of spectacle and power of the lens of spectacle. Recall the various defects of vision of the human eye. Explain these defects with the help of the focal lengths of the spectacles used by the person in the when he is myopic and in his old age.

Formula used:
The focal length $f$ is given by
$f = \dfrac{1}{P}$ …… (1)
Here, $P$ is the power of the lens.

Complete step by step answer:
We have given that the a myopic person is using the spectacles of power $1\,{\text{D}}$. The power of the spectacles of a myopic person is negative.
$P = - 1\,{\text{D}}$
The myopic person cannot see the object placed at large distances.
Hence, the focal length of the eye of the person is
$f = \dfrac{1}{{ - 1\,{\text{D}}}}$
$\Rightarrow f = - 1\,{\text{m}}$
$\Rightarrow f = - 100\,{\text{cm}}$
This focal length gives the far point of the person.
Hence, this myopic person by using the spectacles recommended by the doctor forms the image of the objects which are placed at infinity at a distance of $100\,{\text{cm}}$.
The person with a normal vision has the near point of $25\,{\text{cm}}$.
Therefore, the person using the power of accommodation of the eye-lens is able to see the objects placed at a distance from $25\,{\text{cm}}$ to $100\,{\text{cm}}$.
But in old age, the ability of accommodation is lost with age.
Hence, the same person cannot see the objects placed even at distance $25\,{\text{cm}}$.
This defect of the human eye of being not able to see the nearby objects is known as presbyopia.He uses another spectacle for reading of power $+ 2\,{\text{D}}$.
The focal length for this spectacle is
$f = \dfrac{1}{{ + 2\,{\text{D}}}}$
$\Rightarrow f = 0.5\,{\text{m}}$
$\therefore f = 50\,{\text{cm}}$
The focal length of these other spectacles is $50\,{\text{cm}}$.

From this calculation, we can understand that the person with presbyopia who cannot see the objects at $25\,{\text{cm}}$ distances is suggested to use the spectacle with power $+ 2\,{\text{D}}$ to increase his distance of clear vision.

Note: We have taken the power of the spectacle of the myopic person negative because the lens used in the spectacle used by the myopic person is a concave lens and the focal length of the concave lens is negative. Also, one should keep in mind that a diopter is SI unit of power of lens. Hence, the focal length obtained from the calculation is in SI unit of length which is meter.