Here, we’ll show you how to draw a ray diagram for a concave mirror when the object is outside the center of curvature.

Ray Diagrams for a Concave

MirrorCase 1

In a concave mirror, this is the shiny side of the mirror

This is the shiny side of the mirrors

Here is the principal axis going through the middle of the mirror

The Principal Axis

Here is the focal point F for this mirror

The Focal Point F

×F

×

The 2F point is twice as far from the mirror surface as the focal point, and it is shown here.

2F

The 2F Point

×F

×

The 2F point is also called the center of curvature, C. If the arc of the mirror was extended to form a complete circle, point C would be the center of this circle.

CThe Center

of Curvature

×F

×

We’ll use a yellow arrow for our object and place it on the principal axis. In this example the object is farther from the mirror than the center of curvature, point C.

×FC

The Object

×

We start by drawing a line straight from the top of the object to the surface of the mirror (click). It must be parallel to the principal axis.

×FC

The Object

×

Now we bounce this ray off of the surface and extend it down through the focal point (click) like this

×FC

×

Next we draw a line from the top of the object, straight through the center of curvature, C and strike the surface of the mirror

×FC

×

Because this ray is going through the center of curvature, it will bounce straight back on the same path.

×FC

×

The point where these two reflected rays from the top of the object cross will be the top of the object in the image.

×FC

This will be the top of the object in the image

×

Remember, the bottom of the object is sitting on the principal axis.

×FC

This will be the top of the object in the image

The bottom of the object is on

the principal axis

×

So the bottom of the object in the image will also touch the principal axis, here at a point directly above the top of the object.

×FC

This will be the top of the object in the image

The bottom of the object in the image is also on the principal

axis

×

Now that we know where the bottom and top of the image will be, we can draw the image in (click).

×FC

This will be the top of the object in the image

The bottom of the object in the image is also on the principal

axis

We can use this diagram to summarize the characteristics of an image formed by a concave mirror when the object is outside of the center of curvature, C.

Object

Image

When the object is outside the center of curvature of a concave mirror:

1. The image is smaller than the object

2. The image is inverted3. The image is between the

center of curvature and the focal point in front of the mirror

4. The image is a real image

You can see from the diagram that the image is smaller than the object

Object

Image

When the object is outside the center of curvature of a concave mirror:

1. The image is smaller than the object

2. The image is inverted3. The image is between the

center of curvature and the focal point in front of the mirror

4. The image is a real image

Also, the image is upside down, or inverted.

Object

Image

When the object is outside the center of curvature of a concave mirror:

1. The image is smaller than the object

2. The image is inverted3. The image is between the

center of curvature and the focal point in front of the mirror

4. The image is a real image

The position of the image is between the center of curvature and the focal point in front of the mirror, on its shiny side

Object

Image

When the object is outside the center of curvature of a concave mirror:

1. The image is smaller than the object

2. The image is inverted3. The image is between the

center of curvature and the focal point in front of the mirror

4. The image is a real image

And because the image is formed by solid rays that cross each other, this is a real image. If the sensor of a digital camera was place here, the image would be recorded on it.

Object

Image

When the object is outside the center of curvature of a concave mirror:

1. The image is smaller than the object

2. The image is inverted3. The image is between the

center of curvature and the focal point in front of the mirror

4. The image is a real image