In this explainer, we will learn how to identify the optical properties of concave lenses.
A lens is a piece of transparent material, with a particular shape, that 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 concave 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 a cylinder. If we view this cylinder from the side, it looks like a rectangle; we are not able to see either of the cylinder’s circular ends. This is shown below.
Now imagine two spheres, one at either end of this cylinder. Viewed from the side, these two spheres look like two circles, as shown below.
Now imagine that these three shapes overlap each other. Viewed from the side, this would look like what is shown in the diagram below.
The shape of a concave lens is what we would get if we were to “cut away” from the cylinder the area where the two spheres overlap it.
We can describe a concave lens as being thinner in the middle and thicker at the edge, as shown below.
Example 1: Identifying a Concave Lens
Which of the following is a concave lens?
A concave lens is a piece of transparent material that has two curved surfaces and that is thinner in the middle and thicker at the edge.
The lenses shown in choices A and B have straight sides, so it cannot be either of them.
The lens shown in choice C has two curved sides, but it is thicker in the middle and thinner at the edge.
This leaves the lens shown in choice D which has two curved sides and is thinner in the middle and thicker at the edge. Choice D shows a concave lens.
There are several terms that are useful for describing the shape of a concave lens. Let’s think again about the shape of a concave lens as formed by two circles, as shown below.
The concave lens is now shown in light blue. The two 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 radius 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 Concave Lens
The diagram shows a concave lens. Which line shows the optical axis of the lens? Assume that light rays pass through the lens traveling in the vertical direction.
This concave lens has been oriented differently to how we usually see concave lenses oriented. We usually see concave lenses oriented like in the diagram below.
Recall that the shape of a concave lens can be made using two circles, 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 orient the lens in the same way 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 1.
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 concave lens.
Before the rays enter the lens, they are parallel. After the rays exit the lens, they spread out.
If we were to trace the lines of the refracted rays back through the lens, the lines would meet at a point. This is shown in the diagram below.
This point is known as the focus or focal point of the lens. (The plural of “focus” is “foci.”) The distance between the focus of a lens and the center of the lens is known as the focal length. This is shown on the diagram below.
When rays of light spread out away from a point like this, we say that they are diverging. The diagram below shows diverging light rays.
Because concave lenses can make rays diverge, they are sometimes called diverging lenses.
Example 3: Identifying Diverging Rays
Which of the following diagrams shows light rays diverging from a point?
Recall that light rays are said to be diverging if they spread out away from a point as time passes.
Choices B, C, and D do not show diverging rays, as the rays stay the same distance apart.
Choice A does not show diverging rays, as the arrows indicate that the rays are moving toward a point, getting closer together as time passes.
Choice E shows rays getting further apart as time passes, spreading out away from a point. Therefore, choice E shows diverging rays.
- A concave lens is a piece of transparent material with the shape shown below.
- A concave lens can cause light rays to spread out away from a point.
- If light rays spread out away from a point as time passes, we say that they are diverging.