Question

Calculate maximum power of accommodation of a person having normal vision.

Answer 1

Use the formula for the power of a lens. This formula gives the relation between the power of a lens and the focal length of the lens.

Formula used:

The power of a lens is given by the equation
$P = \dfrac{1}{f}$ …… (1)

Here, $P$ is the power of the lens and $f$ is the focal length of the lens.

Complete step by step answer:
The distance for which a normal person with a normal eye vision can see is 25 cm.

Hence, the focal length of a lens in the eye of a normal person is 25 cm.

Calculate the maximum power of accommodation of a person having normal vision.

The power of one diopter is equal to 100 cm.

Substitute $25\,{\text{cm}}$ for $f$ in equation (1).
$P = \dfrac{1}{{25\,{\text{cm}}}}$
$\Rightarrow P = \dfrac{{1\,{\text{D}}}}{{25\,{\text{cm}}}}$

The power of one diopter is equal to 100 cm.

Substitute $100\,{\text{cm}}$ for $1\,{\text{D}}$ in the above equation.
$\Rightarrow P = \dfrac{{100\,{\text{cm}}}}{{25\,{\text{cm}}}}$
$\Rightarrow P = 4\,{\text{D}}$

Hence, the maximum power of accommodation of a person having normal vision is $4\,{\text{D}}$.

Additional information:

The ability of the pupil of the eye to change its diameter by which the focal length of the eye lens is adjusted by the ciliary muscles for the retina to see the near or distance object clearly is known as the power of accommodation of the eye.

Note: Since the focal length is in centimeter, the numerator of the power of lens formula is multiplied by 100. If the focal length is in millimeter, the numerator of the power of lens formula is multiplied by 1000.