Question

Find the maximum and minimum focal length of the eye lens?

Answer 1

Step 1: Focal Length

1. The distance between the optical center and the lens's focus is known as the focal length of a spherical lens.
2. A lens' focal length is half its radius of curvature.

Step 2: Formula used

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ ………. eq ( i ) [ where u = object distance, v = image distance , f =focal length ]

Step 3: Maximum focal length

An object is at infinity at the time of maximum focal length.

We know that the distance between the lens and the retina is 2.5 cm and that the picture will form at the retina, hence $v=2.5cm$.

Hence, in the case of maximum focal length $u=-\infty ,v=2.5cm$

Putting these values of u and v in eq ( i )

$$\begin{gathered} \frac{1}{2.5}-\frac{1}{-\infty }=\frac{1}{f_{max}} \\ \frac{1}{2.5}+0=\frac{1}{f_{max}} \\ {f}_{max}=2.5cm \end{gathered}$$

Step 4: Minimum focal length

For minimum focal length, the object distance is 25 cm ( least distance of distinct vision ).

$u=25,v=2.5cm$

Putting these values of u and v in eq ( i )

$$\begin{gathered} \frac{1}{2.5}-\frac{1}{-25}=\frac{1}{f_{min}} \\ \frac{1}{2.5}+\frac{1}{25}=\frac{1}{f_{min}} \\ {f}_{min}=\frac{25}{11} \\ {f}_{min}=2.27cm \end{gathered}$$

Hence the maximum focal length is 2.5 cm and the minimum focal length is 2.27 cm.