Question

A nearsighted person has a far point of 40cm. What power spectacle lens is needed if the lens is 2cm from the eye

Answer 1

The value is
`p = - 2.63 \ Diopters`

Step-by-step explanation:

From the question we are told that

The value of the far point is
`a = 40 \ cm = 0.4 \ m`

The distance of the lens to the eye is
`b = 2 \ cm = 0.02`

Generally

`1 Diopter = > 1 m^(-1)`

Generally the power spectacle lens needed is mathematically represented as

`p = (1)/(d_o ) + (1)/(d_i)`

Here
`d_o` is the object distance which for a near sighted person is
`d_o = \infty`

And
`d_i` is the image distance which is evaluated as

`d_i = b - a`

=>
`d_i = 0.02 - 0.4`

=>
`d_i = -0.38 \ m`

So

`p = (1)/(\infty ) + (1)/(-0.38)`

=>
`p = 0 - 2.63`

=>
`p = - 2.63 \ Diopters`