Question

A typical person's eye is 2.5 cm in diameter and has a near point (the closest an object can be and still be seen in focus) of 25 cm, and a far point (the farthest an object can be and still be in focus) of infinity.
1) What is the minimum effective focal length of the focusing mechanism (lens plus cornea) of the typical eye?
2) What is the maximum effective focal length of the focusing mechanism (lens plus cornea) of the typical eye?

Answer 1

Answer:

2.27 cm

2.5 cm

Explanation:

u = Object distance =  25 cm

v = Image distance = 2.5 cm

f = Focal length

Lens Equation

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\\\Rightarrow \frac{1}{f}=\frac{1}{25}+\frac{1}{2.5}\\\Rightarrow \frac{1}{f}=\frac{11}{25}\\\Rightarrow f=\frac{25}{11}=2.27\ cm$

The minimum effective focal length of the focusing mechanism of the typical eye is 2.27 cm

when $u=\infty$

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\\\Rightarrow \frac{1}{f}=\frac{1}{\infty}+\frac{1}{2.5}\\\Rightarrow \frac{1}{f}=\frac{1}{2.5}\\\Rightarrow f=\frac{2.5}{1}=2.5\ cm$

The maximum effective focal length of the focusing mechanism of the typical eye is 2.5 cm