The following drawing of a simple lens will serve to illustrate basic optics terms.
The lens in the drawing is a “positive lens“, which is defined as a lens that forms an image that can be shown on a screen. Simple magnifying glasses are positive lenses. Negative lenses also exist, but the image is on the same side of the lens as the object, so putting a screen there would make it impossible for light to get to the lens. That’s why the image formed by negative lenses can’t be shown on a screen.
The black line on the left side of the drawing symbolizes the object, which is whatever the lens is looking at. The black line on the right side of the image symbolizes the image. You could put a screen (e.g. a white piece of paper) there and see a copy of the object. As you can see from the picture, the image formed by a simple lens is upside-down. Get a magnifying glass and a piece of paper, and try it yourself!
The distance from the lens to the object is called the “object distance“. Similarly, the distance from the lens to the image is called the “image distance“. These distances are measured along the horizontal dash-dot line from the bottom of the object through the center of the lens. This line is known as the optical axis.
The red and blue line segments are known as the marginal ray and the chief ray. The chief ray always starts at the edge of the object and passes through the center of the lens and the outside edge of the image. Marginal rays always start at the intersection of the optical axis and the object and pass through the edge of the lens and the center of the image. Many other rays could be defined, but knowing the paths of these two rays through any optical system is sufficient to describe all of its basic properties.
In the drawing, the object distance is finite, so the most common way to specify the size of the object is to define the object height. This is the distance from the optical axis to the edge of the object. It is also equal to the height of the chief ray on the object. When the object distance is infinite (or at least very large), it is more reasonable to specify the object angle, which is the angle between the chief ray and the optical axis. One could also specify the object angle for a finite object distance, but this is less common. Image height is defined as the distance from the optical axis to the edge of the image.
The magnification of an optical system is defined as the image height divided by the object height. Technically, the image height for a simple lens is negative because the image is inverted, but this detail is sometimes overlooked. If you look carefully at the drawing, you can see similar triangles formed by the optical axis, the chief ray and the object and image. Based on this, we can see that the magnification is also equal to the image distance divided by the object distance, assuming we get the signs right (to an optical engineer, distance is positive to the right, so the object distance in the picture is negative).
For systems commonly used with an infinite object distance, such as telescopes, angular magnification is defined as the object angle divided by the image angle. The latter is the angle between the chief ray and the optical axis in the vicinity of the image. For a simple lens, the angular magnification is always 1, but for a telescope it can be 100X or more.
The final basic optics term we’ll define here is focal length, which is equal to the image distance when the object is at infinity. If the object is a finite distance away and both the object and image distances are known then the thin lens equation below can be used to determine the focal length. Keep in mind that the object distance “s” is measured from the lens surface which means that “s” as drawn above is a negative quantity.
Oops! I forgot one. Here’s one more basic optics term: the f/# (pronounced “eff number”). The f/# of a simple lens is the focal length of the lens divided by its diameter. It is a measure of how much light can get through a lens. Because the lens diameter is in the denominator (the bottom of the fraction), a larger diameter results in a smaller f/#. So an f/2 (pronounced “eff too”) lens collects more light than an f/4 lens. Photographers say that an f/2 lens is “faster” than an f/4 lens because it collects light onto the film or detector more quickly. Take a look at this page to learn more about f/# and numerical aperture.