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

Answer:

The value is $p = - 2.63 \ Diopters$

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

           $p = \frac{1}{d_o } + \frac{1}{d_i}$

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

         $p = \frac{1}{\infty } + \frac{1}{-0.38}$

=>      $p = 0 - 2.63$

=>      $p = - 2.63 \ Diopters$