Question

The far point of a myopic person is $150cm$ in front of the eye. Calculate the focal length and power of the lens required to enable him to see distant objects clearly.

Answer 1

Step 1: Given data

1. Image distance, $v=-150cm$
2. Object distance, $u=-\infty$, because objects can be seen from a large distance clearly

Step 2: Expression for the focal length is shown below

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

Here $v$ is image distance and $u$ is object distance.

Step 3: Calculate the focal length,

Substitute $-150cm$ for $v$ and $-\infty$ for $u$ in above expression of the focal length.

$$\begin{gathered} \frac{1}{f}=\frac{1}{-150cm}-\frac{1}{-\infty } \\ =-\frac{1}{150cm}-0 \\ =-\frac{1}{-150cm} \\ f=-150cm \end{gathered}$$

Step 4: Expression for the power of the lens is shown below

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

Here $f$ is focal length in m.

Step 5: Calculate the power of the lens,

Substitute $-150cm$ for $f$ in above expression for focal length.

$$\begin{gathered} P=\frac{1}{-150cm} \\ =-\frac{100}{150}D \\ =-0.67D \end{gathered}$$

Hence required focal length is $-150cmor-1.5m$ and power is $-0.67D$.