In this explainer, we will learn how to identify the optical properties of convex lenses.
A lens is a piece of transparent material that has a particular shape and can be used to change the direction that light rays are traveling in.
Recall that a transparent material is one that allows light to pass through it—in other words, it is see through. Two examples of transparent materials are glass and perspex, both of which are often used to make lenses.
A convex lens is a lens with a shape that when viewed from the side looks like the shape shown below.
To understand this shape, first, imagine two spheres. Viewed from the side, these two spheres would look like two circles, as shown below.
Now, imagine that these two spheres overlap each other. Viewed from the side, this would look like two overlapping circles, as shown below.
The area where the two spheres—or circles—overlap is the shape of a convex lens.
We can describe a convex lens as being thicker in the middle and thinner at the edge, as shown below.
Example 1: Identifying a Convex Lens
Which of the following is a convex lens?
A convex lens is a piece of transparent material that has two curved surfaces and is thicker in the middle and thinner at the edge.
Both B and D only have straight sides, so it cannot be either of them.
A has two curved sides, but it is thinner in the middle and thicker at the edge.
That leaves choice C, which has two curved sides and is thicker in the middle and thinner at the edge. Choice C shows a convex lens.
There are several terms that are useful for describing the shape of a convex lens. Let’s think again about the shape of a convex lens as two overlapping circles, as shown below.
The convex lens is now shown in light blue. The two overlapping circles are now shown in orange. The two magenta dots show the centers of the two circles. There is a special term for these two magenta dots—they are called the centers of curvature of the lens.
The same diagram is shown below but with two red arrows on it.
The red arrows show the radii of each circle. There is a special term for these radii—they are called the radii of curvature. (Remember that “radii” is just the plural of “radius.”)
The same diagram is shown below but with a black dashed line from one center of curvature to the other.
This line is called the optical axis of the lens. The optical axis passes through both centers of curvature of the lens as well as the center of the lens.
The optical axis is also called the principal axis.
All of these points and lines are labeled on the diagram below.
Example 2: Identifying the Optical Axis of a Convex Lens
The diagram shows a convex lens. Light rays pass through the lens in the vertical direction. Which line shows the optical axis of the lens?
This convex lens has been orientated differently from how we usually see convex lenses. We usually see convex lenses orientated like in the diagram below.
Recall that the shape of a convex lens is the same as the area where two circles overlap, as shown below.
The optical axis is a line that passes through the center of each circle and the center of the lens, as shown below.
However, in order to orientate the lens in the same way as shown in the question, we must rotate the lens shown in the above diagram by . This is shown below.
Comparing this diagram to the one given in the question, we can see that the optical axis of the lens is line 2.
Lenses can change the directions of light rays that pass through them. This process is known as refraction.
The diagram below shows what happens when parallel light rays, indicated by the red lines, enter a thin convex lens.
Before the rays enter the lens, they are parallel. After the rays exit the lens, they get closer together and eventually meet at the point labeled P.
The rays are focused at a point by the lens.
This is a very useful property of convex lenses. The point P is known as the focus or focal point. (The plural of “focus” is “foci.”) The distance between the focus of a lens and the center of a lens is known as the focal length. This is shown on the diagram below.
When rays of light get closer together and meet at a point like this, we say that they are converging. The diagram below shows converging light rays.
Because a convex lens can make rays converge, convex lenses are sometimes called converging lenses.
Example 3: Identifying Converging Rays
Which of the following diagrams shows light rays converging on a point?
Recall that light rays are said to be converging if they get closer together over time and meet at a point.
Choices B, C, and D do not show converging rays, as the rays stay the same distance apart.
Choice A does not show converging rays, as the arrows indicate that the rays are moving away from a point, getting farther apart as time passes.
Choice E shows rays getting closer together as time passes, meeting at a point. Therefore, choice E shows converging rays.
- A convex lens is a piece of transparent material with the shape shown below.
- A convex lens can focus light rays at a point.
- If light rays get closer together over time and meet at a point, we say that they are converging.