Question

Derive the formula to calculate the focal length of a lens used for correcting a myopic eye.

Answer 1

Step 1: Myopia

Myopia is the defect of vision due to which the eye cannot see far-off objects clearly but can see nearby objects distinctly.
It can be treated by using spectacles made from concave lenses of appropriate focal length.

Step 2: Finding the focal length of a lens used for correcting a myopic eye.

The concave lens needed to correct a myopic eye should form the image of the far-off object at the far point $\left(d\right)$ of the myopic person.
As per sign conventions,
The object distance is $u=-\infty$
The image distance is $v=-d$
According to the lens formula,

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

where $f$ is the focal length of the lens.

Substituting the known values

$$\begin{gathered} \frac{1}{f}=\frac{1}{\left(-d\right)}-\frac{1}{\left(-\infty \right)} \\ \frac{1}{f}=-\frac{1}{d} \\ f=-d \end{gathered}$$

Therefore, the focal length of the corrective concave lens should be equal to the distance of the far point from the eye.