# Lesson Explainer: Drawing Ray Diagrams for Convex Lenses Science

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

A convex lens focuses parallel light rays at a focal point. This is shown in the following figure.

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 Convex Lens

Any light ray that passes through the center of a convex 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.

Recall that the optical axis of a convex lens is an imaginary line that passes through the center of curvature of the lens and through the widest part of the lens, as shown in the following figure.

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

A light ray that is parallel to, but not along, the optical axis will change direction when it passes through a convex lens. The direction of the light ray will change so that the ray passes through the focal point of the lens that is on the opposite side of the lens to the side that light enters the lens from.

Let us look at some examples involving light rays passing through a convex lens.

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

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

### Answer

Option 2 shows a convex lens that has no effect on the paths of light rays. We see that these light rays do not cross each other. This means that these rays do not all pass through a single point, which they must do when shown correctly.

Option 1 shows the light rays changing direction. We see, though, that these light rays also do not cross each other. This means that these rays do not all pass through a single point, which they must do when shown correctly.

Option 5 shows the light rays changing direction. We see also that these light rays all cross each other. However, the light rays do not all cross each other at the same point, which they must do when shown correctly.

Option 3 shows parallel light rays spreading out after passing through the lens. This would not occur for a convex lens.

The correct answer is option 4, as this shows the light rays all crossing at a single point, which is the focal point of the lens.

### Example 2: Identifying the Path of a Light Ray That Passes through a Convex Lens

Each of the following diagrams shows a ray entering a thin convex 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 and 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 2 and 3, the light ray passes through the center of the lens and changes direction.

Only option 1 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 Convex Lens

Each of the following diagrams shows a ray entering a thin convex 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 and it passes through the center 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 to pass through the focal point of the lens.

Only option 2 shows this light ray passing through the focal point though, so it is the correct option.

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

If an object is further from a convex lens than the focal length of the lens, the light rays from the object that pass through the lens will form an image on the opposite side of the lens to the object.

The image formed can be projected onto a screen. This kind of image is called a real image. The formation of an image is shown in the following figure.

The diagram showing the image is produced by comparing two light rays from the top of the object: a light ray that is parallel to the optical axis and a light ray that passes through the center of the lens.

Let us now look at an example involving a light ray that passes through the center of a convex lens but not along the optical axis.

### Example 4: Identifying the Path of a Light Ray That Passes through a Convex Lens but Not along the Optical Axis

Each of the following diagrams shows a ray entering a thin convex lens. The point marked P is the focal point of the lens. The ray passes through the center of the lens. Which diagram correctly shows the path of the ray after it has passed through the lens?

### Answer

A light ray that passes through the center of a lens will not change direction. This is true whether or not the ray is along the optical axis.

This is only shown in option 3, which is the correct option.

We see that two light rays from the top of the object, after passing through the lens, eventually reach the same point.

This is actually true for light rays from the top of the object that travel in any direction, assuming that these rays first pass through the lens.

What is true for light rays from the top of the object is true for all the other points on the object. This means that every point of the object appears in the image.

It is important to notice that the top of the object is above the optical axis of the lens. The top of the image is below the optical axis of the lens. This means that the image is upside down compared to the object. The image is inverted.

The point at which the image can be seen depends on the focal length of the lens and the distance of the object from the lens.

Changing the distance of the object from the lens changes the distance of the image from the lens.

The size of the image also changes when the distance between the object and the lens changes.

These changes are shown in the following figure.

We see that when the distance between the object and the lens is greater than twice the focal length, the image is smaller than the object.

For distances greater than twice the focal length, moving the object further from the lens will make the image smaller. Moving the object nearer the lens will make the image size become closer to the object size.

At exactly twice the focal length, the object and image will be of equal sizes.

When the distance between the object and the lens is greater than the focal length but less than twice the focal length, the image is larger than the object. This means that the image is magnified. Moving the object closer to the focal point will make the image larger, increasing the magnification.

This following figure shows what happens when the object is at the focal length of the lens.

The light rays from the top of the object are parallel after they exit the lens. These rays do not cross each other.

One way of describing this is that the image formed by this lens forms infinitely far from the lens. This means that for any finite distance from the lens, no image is formed.

The object can still be moved closer to the lens, however.

If the object is moved closer to the lens than the focal length, the two rays that were parallel when the object was at the focal length increase their distance from each other the greater their distance from the lens. This is shown in the following figure.

The fact that these rays increase the distance between them in the space to the right of the lens means that the distance between the paths of these rays must decrease if they were extended into the space to the left of the lens. This is shown in the following figure.

At a point to the left of the object, the extended paths of the rays that exit the lens meet.

The new point is the top of another image that the lens can produce. This is shown in the following figure.

The image formed is not a real image. It cannot be projected on a screen. It is a virtual image. Such an image can be seen, though, by a human eye.

We see that the virtual image is on the same side of the lens as the object, further from the lens than the object.

We also see also that the virtual image is larger than the object.

Moreover, we see that the directions of light rays from the top of the object after passing through the lens are the same as the directions of the lines from the top of the virtual image to the lens.

This means that the virtual image is the same way up as the object.

Let us now summarize what we have learned in this explainer.

### Key Points

• A convex lens can focus parallel light rays that pass through it at a focal point.
• The distance from the lens to the focal point is the focal length of the lens.
• A convex lens only focuses light rays at a point if these rays start from a point further from the lens than the focal length of the lens.
• An object at a distance from the lens greater than the focal length produces a real image on the opposite side of the lens to the object.
• The real image formed by a convex lens is inverted.
• The distance of the object from a convex lens and the focal length of the lens determine the size and the position of the real image formed. The real image may be either larger than, smaller than, or equal in size to the object.
• An object at a distance from a convex lens less than the focal length produces a virtual image rather than a real image.
• The virtual image formed by a convex lens is the same way up as the object that produces it.
• The virtual image formed by a convex lens is larger than the object that produces it.

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