Question

A far-sighted person can see objects beyond 71 cm clearly, if the separation between glasses and eye lens is 2 cm, then find the focal length of the glass?

Answer 1

Step 1: Given data

The person can see beyond $71cm$ clearly

We have given the separation between glasses and eye lens is $d=2cm$.

Step 2: Formula used

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}[\hspace{0.17em}As,f=focallength,v=objectdis\tan ce,u=imagedis\tan ce]$

Step 3: Calculating the focal length of the glass

We have given that the person can see beyond $71cm$ clearly which means for the object placed at a distance of distinct vision ($25cm$), the image should be formed at $71cm$ from the eye. We have given the separation between glasses and eye lens is $d=2cm$. Therefore, the object distance from the lens is, $u=-(25-2)=-23cm$ and the image distance is, $v=-(71-2)=-69cm$

Here the object is placed on the left side of the image, which is taken as negative according to standard sign convention.

Substituting the value of u and v in the formula

$$\begin{gathered} \frac{1}{f}=\frac{1}{v}-\frac{1}{u} \\ \frac{1}{f}=\frac{1}{-69}-\frac{1}{-23} \\ \frac{1}{f}=\frac{2}{69} \\ f=\frac{69}{2} \\ f=34.5cm \end{gathered}$$

Hence, the focal length is $34.5cm$.