Question

: A mother sees that her child’s contact lens prescription is 0.750 D. What is the child’s near point?

Short answer

The child's near point is -0.308 m.

Step-by-step solution

How do contact lenses work?

Contact lenses operate by bending light to bring it into focus on the retina, where vision receptors collect data and send it to the brain.

Given information and Formula to be used

P= 0.750 D

You know that the near point for a normal relaxed eye is 0.25 m.

The power of the lens is equal to the reciprocal of the focal length is :

$$\begin{gathered} \mathrm{P}=\frac{1}{\mathrm{f}} \\ \mathrm{P}=\frac{1}{{\mathrm{d}}_0}+\frac{1}{{\mathrm{d}}_1} \end{gathered}$$

What is the child's near point?

Rearrange the distance between the close point and the child's eyes and solve for it:

Equation (1) is obtained by substituting data values.

$$\begin{gathered} \frac{1}{{\mathrm{d}}_0}=\mathrm{P}-\frac{1}{{\mathrm{d}}_{\mathrm{i}}} \\ {\mathrm{d}}_0=\mathrm{P}-\frac{1}{{\mathrm{d}}_{\mathrm{i}}} \\ =\frac{1}{0.750\mathrm{D}-{\displaystyle \frac{1}{0.25\mathrm{m}}}} \\ {\mathrm{d}}_0=-0.308\mathrm{m} \\ \mathrm{Therefore},\mathrm{according}\mathrm{to}\mathrm{the}\mathrm{result},\mathrm{the}\mathrm{child}\text{'}\mathrm{s}\mathrm{near}\mathrm{point}\mathrm{is}-0.308\mathrm{m}. \end{gathered}$$