Optics Problem #0076


626.

Problem 44.37 (RHK)

Parallel rays entering a relaxed eye gazing at infinity produce a real, inverted image on the retina. The eye thus acts as a converging lens. Assume a focal length for the eye of 2.50 cm. An object is moved to a distance from the eye. To form an image on the retina the effective focal length of the eye must be reduced to . This is done by the action of the ciliary muscles that change the shape of the lens and thus the effective focal length of the eye. (a) We have to find from the above data. (b) We have answer in the process whether the radii of curvature of the lens become larger or smaller in the transition from observing infinity to a finite distance.

Solution: Click For PDF Version
We find

using the thin lens equation with values

and

We have

We answer next the second part of the problem. For a converging lens, the focal length f is determined in terms of the radii of curvature and by the lens maker’s formula:

As the focal length of the eye lens gets reduced from 2.5 cm to 2.34 cm in shifting eye from seeing a far object to seeing a near object, the radii of curvature of the eye lens will become smaller.