Question

Repeat the previous problem for glasses that are 2.20 cm from the eyes.

Short answer

The child's near point is 0.297 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= 0.750D

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,

$$\begin{gathered} P=\frac{1}{f} \\ P=\frac{1}{d_0}+\frac{1}{d_i} \end{gathered}$$…………………..(1)

What is the child's near point?

Rearrange the distance between the far point and the person's eyes and solve equation (1) for it, where we obtained after substituting data values,

$$\begin{gathered} \frac{1}{d_0}=P-\frac{1}{d_i} \\ {d}_0=\frac{1}{P-{\displaystyle \frac{1}{d}}} \\ =\frac{1}{0.750D-{\displaystyle \frac{1}{\left(0.25m-0.022m\right)}}} \\ {d}_0=0.275m \end{gathered}$$

Solve for the glasses that are 2.2 cm, we will get

$$\begin{gathered} d_0=x-2.2cm\left(\frac{1m}{100cm}\right) \\ x=d_0+0.22m \\ x=0.275m+0.22m \\ x=0.297m \end{gathered}$$

Therefore, the near point for the child is 0.297 m.