Question

how do you decide the focal length of concave lens required to correct the detect of myopic eye?​

Answer 1

To explain:

How to decide the focal length of a concave lens required to correct the defect of myopic eye?

Detailed Discussion:

First of all , let's know what is myopia ?

• It is an ocular defect in which the person is unable to see far away objects clearly. However he/she can clearly see nearby objects.

• This is because the light rays coming from distant objects after getting refracted from eye lens meet the principal axis before the retina.

Hence, we use Bi-Concave lens to correct this defect , such that the light rays will be diverged and it will be reaching the retina.

Now, how to find the focal length of the lens to be used ?

• In this defect , the far-point of the eye comes closer that infinity.

• So, we need to use a a concave lens such that light rays from the distant objects will produce a virtual image at the new far point of the eye.

• This virtual image will act as an object and will produce a proper image at the retina.

Let focal length of lens be f and new far-point be x:

$\sf \therefore \: \dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}$

$\sf \implies\: \dfrac{1}{f} = \dfrac{1}{( - x)} - \dfrac{1}{ \infty}$

$\sf \implies\: \dfrac{1}{f} = \dfrac{1}{( - x)} - 0$

$\sf \implies\: \dfrac{1}{f} = \dfrac{1}{( - x)}$

$\sf \implies\: f = - x$

So, focal length will be equal to the new far-point of the eye.