Optical Instruments

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.

What is the minimum effective focal length of the focusing mechanism (lens plus cornea) of the typical eye? 

What is the maximum effective focal length of the focusing mechanism (lens plus cornea) of the typical eye?

Answer 1

Using the thin lens equation : 1/f=1/di + 1/do Where di is the image distance and do is the object distance and f is the focal length

In this case di=2.5cm because the image is formed at a distance equal to the diameter of the eye

Do 2 calculations:

Find f for do=25cm

Find f for do= inf.

#1 1/f=1/2.5 + 1/25 => (1/2.5 +1/25)^-1 = 2.27cm = minimum effective focal length of the focusing mechanism (lens plus cornea) of the typical eye.

#2 1/f=1/2.5 + 1/inf => (1/2.5 + 0)^-1= 2.5cm=maximum effective focal length of the focusing mechanism (lens plus cornea) of the typical eye.