Presentation: cameras and eyes

After qualitatively and quantitatively analyzing images generated by lenses, we now apply these concepts to how cameras and eyes work.

First, the similarities between cameras and eyes.

A basic, camera consists of a single converging lens, and here projects a real image onto a ground glass plate. (How do you know that this is a real image?) A film negative, or a charge-coupled device (CCD) can also be placed at this location to capture this image for posterity.

Similarly an eye can be modeled as consisting of a single converging lens, projecting a real image on the retina, on the back of the eye. (How do you know that this is a real image?) Rod and cone cells at this location capture this image and sends it to the brain.

Second, key differences between cameras and eyes.

A camera would need to focus on objects at different d_o distances, here by default focused on a distant object (large d_o). With a fixed focal length lens, f is constant on the right side of the thin lens equation, such that in order to focus on nearby objects, decreasing d_o on the left side of the equation must increase the image distance d_i, which means the lens of camera must move outwards to increase the lens-to-image distance. Thus a camera initially focused on a distant object must move its lens outwards in order to focus on a nearby object.

An eye would also need to focus on objects at different d_o distances, here by default focused on a distant object (large d_o). However, the image distance d_i must remain constant (as the size of the eye cannot change). In order to focus on nearby objects, decreasing d_o on the left side of the thin lens equation means that on the right side of the equation, the focal length f must also decrease! The eye can do this by accommodation, where the ciliary muscles contract, changing the curvature of the lens, decreasing its focal length f. Thus a relaxed eye focused on a distant object must "squish" its lens in order to focus on a nearby object. You can feel the effort the ciliary muscles in your eye exert during accommodation if you force yourself to focus extremely close-up.

Third, common vision defects.

Normal vision consists of being able to focus on different object distances. Nominally the far point value--the farthest object distance that can be sharply focused by a relaxed eye--is infinity (or far away enough that the quantity 1/d_o in the thin lens equation can be considered close enough to zero).

The nominal near point value--the closest object distance that can be sharply focused by an accommodated eye--is 25 cm.

Myopia or "nearsightedness" is the diagnosis for having a normal near point (thus being able to see near), but having some measurably finite far point (thus not being able to see far), due to a defect in the curvature (and focal length) of the eye.

Hyperopia or "farsightedness" is the diagnosis for having a normal far point (thus being able to see far), but having a near point greater than 25 cm (thus not being able to see near), due to a defect in the curvature (and focal length) of the eye. Keep in mind that 25 cm is an arbitrary "reading distance," and young children with flexible lenses and strong ciliary muscles can "squish" and accommodate their eyes to focus on extremely nearby objects, and can have near points less than 10 cm.

Similar to the symptoms of hyperopia is presbyopia or "elderly vision," which is the gradual loss with age of the ability to accommodate and shorten the focal length of the eye to focus on objects as close as 25 cm. This is a natural consequence of aging, and people with normal vision will all eventually experience the loss of accommodation, and must hold reading material farther and farther away as their near points grow longer and longer.

So how would we correct for these vision defects?

Since myopia and hyperopia are both caused by defects in the curvature (and focal length) of the eye, then a radical solution would be to surgically reshape the curvature of the eye.

A more mundane solution to correct for vision defects would be prescribing glasses or contacts, which we will discuss further in the next presentation.