# Lesson Explainer: Drawing Ray Diagrams for Concave Lenses Science

In this explainer, we will learn how to draw diagrams of light rays interacting with concave lenses.

The following figure shows how initially parallel light rays change direction when they pass through a concave lens.

We see that the distances between the light rays become greater the further that the rays travel from the lens.

As the light rays diverge, they do not focus at a point. This means that these light rays do not form a real image that can be projected on a screen.

The fact that the light rays exiting the lens diverge suggests that the paths of these rays would all start from one point on the opposite side of the lens.

This does in fact happen. The point at which the paths of the light rays exiting the lens cross each other is shown in the following figure.

This point is called the focal point of the lens. This is shown in the following figure.

The distance from the center of the lens to the focal point is called the focal length.

The directions of light rays that pass through the lens depend on two rules.

The first rule applies to any light ray that passes through the lens.

### Rule: Refraction of Light Rays on the Optical Axis of a Concave Lens

Any light ray that passes through the center of a concave lens does not change direction.

The second rule applies to light rays that are parallel to the optical axis before they reach the lens and that do not pass through the center of the lens.

### Rule: Refraction of Light Rays off the Optical Axis of a Concave Lens

A light ray that is parallel to, but not along, the optical axis will change direction when it passes through a concave lens. The direction of the light ray will be changed so that the direction of the ray is on a line that passes through the focal point. This point is on the same side of the lens that light rays entered the lens from.

Let us now look at some examples about the focal points of concave lenses.

### Example 1: Identifying the Effect of a Concave Lens on the Paths of Parallel Light Rays

Which of the following diagrams shows what happens when parallel light rays pass through a thin concave lens?

### Answer

Option E shows a concave lens having no effect on the paths of light rays. We see that the directions of these light rays are not along lines that cross each other. This means that lines with the directions of these rays do not all pass through a single point, which they must do when shown correctly.

Option C shows a concave lens making the directions of the light rays passing through it change. Again, we see that the directions of these light rays are not along lines that cross each other. This means that lines with the directions of these rays do not all pass through a single point, which they must do when shown correctly.

Option D shows a concave lens changing the directions of light rays in the same ways as option C, but upward instead of downward. Option D is then incorrect for the same reason as option C.

Option B shows the parallel rays being focused at a point. This point is on the opposite side of the lens to the side from which light rays entered. For a concave lens, the rays themselves do not cross each other.

Option A shows light rays spreading out after passing through the lens. The directions of these rays are along lines that pass through a point on the same side of the lens that the light rays entered from. This is the correct option.

### Example 2: Identifying the Path of a Light Ray that Passes Through a Concave Lens

Each of the following diagrams shows a ray entering a thin concave lens. The point marked P is the focal point of the lens. Before the ray enters the lens, it is parallel to the optical axis. It passes through the center of the lens. Which diagram correctly shows the path of the ray after it passes through the lens?

### Answer

Any light ray that passes through the center of a lens does not change direction. In options B and C, the light ray passes through the center of the lens and changes direction.

Only option A shows the light ray not changing direction. It is the correct option.

### Example 3: Identifying the Path of a Light Ray that Passes Through a Concave Lens

Each of the following diagrams shows a ray entering a thin concave lens. The point marked P is the focal point of the lens. Before entering the lens, the ray is parallel to the optical axis of the lens. Which diagram correctly shows the path of the ray after it passes through the lens?

### Answer

The light ray that enters the lens is parallel to the optical axis but not along the optical axis. This ray does not pass through the center of the lens. The ray must then change direction. The change in direction of the ray must be so that the direction is along a line that passes through the focal point of the lens.

Only option A shows the direction of the light ray along a line passing through the focal point, though, so it is the correct option.

### Example 4: Identifying the Foci of a Concave Lens

The diagram shows a thin concave lens. The lens is symmetrical. The point marked P is one of the foci of the lens. Using the grid, determine which of the points (I, II, III, or IV) is the other focus of the lens.

### Answer

Light rays can pass through the lens from the left side to the right side or in the opposite direction.

The lens is symmetrical, so the effect of the lens on parallel light rays is equivalent in either direction.

The point P is the focal point for light rays passing from the left side to the right side. This point is at a distance equal to the length of 3 squares from the center of the lens.

As the lens is symmetrical, the focal length of the lens is the same either side of the lens.

The point that is at a distance equal to the length of 3 squares from the center of the lens on the right side of the lens is point II.

This is shown in the following figure.

The existence of the focal point for a concave lens means that the light rays exiting the lens can form a virtual image, which could be seen by a human eye.

Such a virtual image is shown in the following figure.

It is important to notice that the object behind the lens can be seen through the lens.

This tells us that the light rays exiting the lens do not actually start from the focal point. The rays all start from different points on the object behind the lens. This is shown in the following figure.

Let us consider an object that has its base at the same height as that of the middle of a concave lens. This is shown in the following figure.

We see a light ray from the top of the object entering the lens parallel to a light ray from the base of the object.

The image formed by the concave lens requires another light ray to be considered. This is shown in the following figure.

We see that the additional light ray considered is also from the top of the object. This ray passes through the center of the lens.

If the focal point of the lens is added to the diagram, the position and size of the image of the object is shown.

We notice that the light rays from the base of the object have the same directions as light rays from the base of the image.

We notice that the light rays from the top of the of the object have the same directions as light rays from the top of the image.

This means that the object and the image are the same way up.

We also see that the image is smaller than the object.

This is what we observe when looking through a concave lens. The following figure shows this.

Let us now summarize what has been learned in this explainer.

### Key Points

• A concave lens diverges parallel light rays that pass through it.
• A concave lens does not focus light rays that pass through it.
• A concave lens has a focal point on the side of the lens from which light passes through.
• A concave lens forms a virtual image.
• The image formed by a concave lens is smaller than the object that produces it.
• The image formed by a concave lens is the same way up as the object that produces it.

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