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 of an eye called myopia (short-sightedness or near-sightedness) is corrected by using spectacles containing concave lens of appropriate focal length.
Here the far point of myopic person is 80 cm. (while far point of normal person is infinity `oo` )
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 own far point (which is 80 cm here).
So, in this case :
Object distance `u = -oo" "`(Normal far point)
Image distance `v = -80 cm" "`(Far point of this defective eye in front of lens)
Focal length f = ?
Now,
By the lens formula,` (1)/(f)=(1)/(v)-(1)/(u)`
`therefore (1)/(f)=(1)/(-80)-(1)/(-oo) `
`therefore (1)/(f)=-(1)/(80) `
`therefore f= -80cm `
= -0.8 m (Concave lens)
Now,
Power of the lens,
` P= (1)/(f)`
` therefore P= (1)/(-0.8 m) `
` = -(10)/(8)m^(-1)`
` = -1.25 D`
A concave lens of power - 1.25 D is required to correct the problem.