Looking at how light gets manipulated by lenses, we can see images that are inverted, fuzzy, or otherwise manipulated by the lens in question.
We use lenses to focus light at a specific point. This ability forms the backbone of how glasses, contact lenses, camera lenses, even telescopes work.
Positive focal length is the distance from the lens to the focused image.
So what is negative focal length?
Negative focal length denotes the distance from the lens to the focal point. But it’s on the other side of the lens — toward the light source and the object whose image is focused at the positive focal length.
Convex, Concave, and Flat Lenses
We find a use for all three kinds of lenses. The most common in our everyday lives is a flat lens, which is what a mirror uses. It reflects light to us in the least manipulated way possible.
A convex lens is thinner at the edges and thicker in the middle. It looks kind of like an American football when viewed from the side. When light hits the lens, it travels through it, and the curve of the lens bends those light rays toward a single point.
The light rays, here represented by gray arrows, travel from the object to the convex lens, from left to right in our diagram. When they leave the lens, they have been redirected and converge at the red dot, the focal point. The distance from the lens to the red dot is its focal length. Here, it’s a positive focal length.
The red dot on the left corresponds to the distance from the lens to the positive focal point. This left dot represents the lens’s negative focal point.
A concave lens is the opposite of convex in every conceivable way. Not only is it thicker at the edges and thinner at the middle, but it also does the opposite to the light rays. It diffuses them, sending them out and away from a focal point in a process called divergence.
The light rays scatter outward, but the focal point, again represented by a red dot here, is on the left side. It’s still a negative focal length, but it often marks the point where the object sits.
In practical terms, let’s think of two common objects: a magnifying glass and a prism. When you look through a magnifying glass, you notice that you have to move it toward and away from your eye before whatever you’re trying to look at comes into focus. In this scenario, your eye is at the negative focal length, and the object you’re looking at is at the positive focal length.
The focal point is also viscerally demonstrated by little kids when they take the magnifying glass outside, focus the sunlight in one spot, and hope to start a fire.
While it’s not a concave lens, a prism can still show the principle: light scatters from it, and in this case, it scatters out in separate wavelengths, which is why we see the rainbow colors coming out of it.
Flat lenses affect the light, less so than the others, but can alter it somewhat — maybe even just slightly change the direction of the light rays. But when we look into a mirror, for example, unless it’s a funhouse mirror, we want to see the most faithful reproduction of ourselves as possible, so we use a flat lens. The light is minimally affected and can travel from us to the mirror and back to our eyes with minimal distortion.
As we’ve discussed, we use lenses to focus light, but how? Why? The lenses most of us know well are those found in glasses and contact lenses.
Eyesight that’s less than 20/20 occurs because the eye has become misshapen, and the retina is no longer in the right place to allow for the image to focus correctly, so we perceive images as being blurry.
When you’re nearsighted, the image focuses in your eye in front of the retina rather than on it. You can see objects close to you clearly but distant objects are blurry.
An optometrist will prescribe a concave lens to fix this, which it does by changing the angle at which light rays enter your eye.
The concave lens spreads the light rays out, essentially forcing the focal point of your eye to occur farther back toward the retina, which allows you to see clearly.
On the opposite end, farsightedness occurs when the eye’s focal point is behind the retina. YOu can see faraway images, but things near at hand are blurry. A convex lens corrects this by focusing light at a shorter distance inside your eye.
Another way we use lenses to focus light is in camera lenses.
We use convex lenses to capture the light rays (which travel in a straight line until they encounter something that alters their trajectory, like a lens).
The lens focuses those rays on a piece of film or a digital receptor and gives us a faithful reproduction of the object the light rays came from.
Negative Focal Length
For all the talk of light rays and convergence and lenses, negative focal length comes down to this: it’s the point from which the light rays diverge.
It is most commonly perceived by looking at the concave lens.
The light coming out of the concave lens is spreading out, and following those rays back to the other side of the lens where they would meet is the spot we call the negative focal point.
There are many uses for lenses, whether looking at cells through a microscope, stars through a telescope, or the New York Times crossword through your reading glasses.
We have learned how to use the properties of light, and the different ways materials affect that light to our benefit.
Understanding that a negative focal point makes eyeglasses work, and this allows us to look out across the universe to learn new things.