Question

The far point of a myopic person is 100 cm in front of the eye. Calculate the focal length and power of the lense required to enable him to see the distant object clearly

Answer 1

According to question we have given;

$u \: = \: - \: \infty$

$v \: = \: - \: 100$
$f \: = \: ?$

$P = ?$

So, formula used here is

$\frac{1}{f}$ = $\frac{1}{v}$ - $\frac{1}{u}$

$\frac{1}{f}$ = $\frac{- 1}{100}$ - $\frac{- 1}{\infty}$

Now,

$\frac{1}{\infty} = 0$

So,

$\frac{1}{f}$ = $\frac{- 1}{100}$

$\textbf{f = - 100 cm}$

Now, f = - 1.0 m

P = $\frac{1}{f}$

P = $\frac{- 1}{1.0}$

P = - 1 D

$\textbf{P = - 1 D}$

As the answer came in negative so the lens used here is $\textbf{Concave lens.}$
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Answer 2

$\frac{1}{f}$Answer:

The focal length and the power of the lenses are

Focal length of a lens: The focal length is the distance of the principal focus from the optical center of a lens.

                  $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$  where v is the image distance and u is the object distance.

Explanation:

Given u = -∞ and v = -100.

Now we have the lens formula as $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ substituting the values we get

                              $\frac{1}{f} = \frac{1}{-100}$

which will give us focal length f = -100cm.

Now the power of the lens P = $\frac{1}{f}$  = -1/1m = -1.0D