14.5 The Eye
By the end of this section, you will be able to:
- Understand the basic physics of how images are formed by the human eye
- Recognize several conditions of impaired vision as well as the optics principles for treating these conditions
Here is a schematic of the human eye:
The cornea and lens form a system that acts like a single thin lens, where most of the refraction occurs when the light from an object transmits from air to the cornea. This is because there is a big difference in the index of refraction between air and the cornea, much more than between the cornea and the lens. For clear vision, a real image must be projected onto the retina, which is a fixed distance from the lens, since the eye does not change in size. The diameter of a human eye is about 1 inch so the image distance, di, is always equal to the distance from the lens to the retina (~ 1 inch).
|The lens in your eye…|
|The image on your retina is always…|
|The image on your retina is always…|
The lens is not infinitely variable, and the human eye cannot focus on objects at all distances. The closest distance at which an object can be focused is called the near point (N).
You can measure your near point right now. Take a ruler and hold it horizontally with one end close to one eye while closing the other eye. Then take something like a pencil or some paper with fine print on it, something small, and hold it next to the ruler. Move the pencil farther away from your eye until it goes out of focus and becomes blurry. Check where it is on the ruler. The distance from your eye to the point where this object went out of focus is called the near point. For young, healthy eyes this distance is somewhere around 15-20 cm. As people get older their near point becomes increasingly far away. I’m old enough now that I can’t use a regular ruler to measure my near point because it’s not long enough. I have to use a meter stick, LOL.
The distance farthest from the eye at which an object can be clearly focused is called the far point. If your far point is not very far away, you are nearsighted and you need corrective lenses.
Consider looking at a fly that is sitting on a wall 3 m away. Let’s say the fly is 0.5 cm long.
1. Draw a ray diagram showing the fly and the image of that fly formed on the back of your retina. What sort of image (real or virtual) is it?
2. We are given the object distance (do = 3 m) and the image distance is implied, since the distance from the lens to the retina is approximately 1 inch (1 in. = 2.54 cm). This means you can calculate the magnification. Do this, and then determine the size of the image on your retina.
3. If we approximate the optical system of the eye as a thin lens, what is the focal length of this lens when you look at a fly 3 m away?
4. The fly flies off the wall and heads right toward you. What does the focal length of the lens in your eye change to if you focus on the fly when it is 10 cm away?
You have probably heard of 20/20 vision. If you have 20/20 vision, you perceive objects crisply without the use of prescription lenses. If you have 20/60 vision, then you must be as close as 20 ft to see what a person with typical vision can see at 60 ft. Or you could have really good vision, like 20/15 vision. This means you see at 20 ft what most people need to be within 15 ft to see clearly.
These differences in vision come down to the shape of our eye and the ability of our ciliary muscles to adjust the thickness of our eye’s lens.
Myopic (Nearsighted) Eye
Hyperopic (Farsighted) Eye
The far point of a certain myopic eye is 50 cm in front of the eye. Find the power of the eyeglass lens that will permit the wearer to see clearly an object at infinity. Assume that the lens is worn 2 cm in front of the eye.
The far point of a myopic eye is nearer than infinity. To clearly see objects beyond the far point, we need a lens that forms a virtual image of such objects no farther from the eye than the far point. Assume that the virtual image of the object at infinity is formed at the far point, 50 cm in front of the eye (48 cm in front of the eyeglass lens). Then when the object distance is ∞, we want the image distance to be -48 cm.
What is the power (in diopters) that will permit this person to clearly see an object at infinity? (Check your answer: -2.1 D)
If a contact lens were used to correct this myopia, what power contact lens would we have to use? (Check your answer: -2.0 D)