The far point of a myopic person is 80 cm in front of the eye. What is the nature and power of the lens required to correct the problem?

Explanation

The defect called myopia is corrected by using a concave lens. So, the person requires concave lens spectacles. We will now calculate the focal length of the concave lens required in this case. The far point of the myopic person is 80 cm. This means that this person can see the distant object (kept at infinity) clearly if the image of this distant object is formed at his far point (which is 80 cm here). So, in this case :
Object distance, `u = oo" "` (Infinity)
Image distance, `v = - 80 cm" "` (Far point, in front of lens)
And, Focal length, `f = ?` `" "` (To be calculated)
Putting these values in the lens formula :
`(1)/(v)-(1)/(u)=(1)/(f)`
we get `(1)/(-80) - (1)/(oo)=(1)/(f)`
or `-(1)/(80)-0 = (1)/(f)" "` (Because `(1)/(oo) = 0`)
`-(1)/(80) = (1)/(f)`
f = - 80 cm
Thus, the focal length of the required concave lens is 80 cm. We will now calculate its power. Please note that the focal length of, - 80 cm is equal to `(-80)/(100)` m or - 0.8 m, Now,
Power, `P = (1)/(f ("in metres")`
`= (1)/(-0.8)`
`=-(10)/(8)`
= - 1.25 D
So, the power of concave lens required is, -1.25 dioptres.