A boy has a near point of 50 cm and a far point of 500 cm. Will a –4.00 D lens correct his far point to infinity?

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.

Near point,$d_{Near}=50cm\left(\frac{1m}{100cm}\right)=0.50m$

Far point,$d_{Far}=500cm\left(\frac{1m}{100cm}\right)=5m$

Power of the lens,$P=-4D$

The power of the lens is given as

$P=\frac{1}{d_o}+\frac{1}{d_i}$……………..(1)

Here,

$d_o$is the distance of the object

$d_i$is the distance of the image

The spectacle lens must have an image 500 cm from the eye for an object very far away to correct the vision of a near-sighted person.

The near-sighted person,$d_i=-500cm$ and$d_0=\infty$

Plugging the values in the above equation (1), will give

$$\begin{gathered} P=\frac{1}{\infty }+\frac{1}{\left(-5m\right)} \\ P=-0.2D \end{gathered}$$

Since the power of the given lens -4D is much greater than the required lens, therefore the lens is too strong for the person.

Hence, no the lens is too strong for the boy thus it will not correct his vision.