# Here, we’ll show you how to draw a ray diagram for a convex mirror.

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Here, we’ll show you how to draw a ray diagram for a convex mirror

In a convex 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

Even though we don’t see the side of the mirror that is not shiny, the right side in this case, the focal point F is still drawn over here in our ray diagram. × F The Focal Point

× The 2F point is twice as far from the mirror surface as the focal point, and it is shown here. × F2F The 2F Point

× This point is also called the center of curvature of the mirror, C. If the arc of the mirror was extended to become a full circle, point C would be the center of that circle. × FC The Center of Curvature

× Here is the object we’ll use in this example. It is a yellow arrow, in which the top is a point and the bottom is sitting on the principal axis. × FC The Object

× We’ll start by drawing a straight line from the top of the object to the surface of the mirror like this (click) × FC The Object

× This ray will reflect off of the surface of the mirror, but we don’t know at what angle. × FC ? This ray will reflect off of the surface

× To find out, we erase this arrow (click) × FC

× and draw a dotted line from this point to the focal point behind the mirror (click) the line is dotted because rays don’t actually travel through the mirror. × FC Draw a dotted line from this point to the focal point behind the mirror

× Then we hold a ruler on the dotted line and extend it with a solid arrow in front of the mirror (click). This shows the angle at which this ray reflects from the surface. × FC Extend this dotted line in front of the mirror with a solid arrow

× Next, we take a ruler and draw a line from the top of the object to the center of curvature behind the mirror. It is solid on the front of the mirror (click) × FC Top of Object Center of Curvature

× But dotted when drawn behind the mirror × FC Top of Object Center of Curvature

× Rays that move directly toward the center of curvature, C, travel toward the mirror (click) × FC

× And are reflected straight back along exactly the same path. × FC

× When our brain sees rays coming toward us, it assumes they are travelling in a straight line from their source, × FC

× so these diverging purple and green rays seem to be coming from a source behind the mirror. × FC These diverging rays seem to be coming from behind the mirror

× The rays from the top of the object both seem to be coming from this point, so this will be the top of the image. × FC The top of the image will be here

× The bottom of the object is here on the principal axis. × FC The top of the image will be here The bottom of the object is on the principal axis

× So the bottom of the image will be here on the principal axis, directly underneath the top. × FC The top of the image will be here The bottom of the object is on the principal axis The bottom of the image is here

× So now that we know where the bottom and the top of the image are, we can draw in the image (click) like this × FC The top of the image will be here The bottom of the image is here

Notice that in this case, the image is smaller than the object Using a Convex Mirror: 1.The image is always smaller than the object 2.The image is never inverted (it is right side up) 3.The image is always behind the mirror inside the focal point 4.The image is always a virtual image The image is smaller than the object

In fact it turns out that in a convex mirror, the image is always smaller than the object. Using a Convex Mirror: 1.The image is always smaller than the object 2.The image is never inverted (it is right side up) 3.The image is always behind the mirror inside the focal point 4.The image is always a virtual image The image is smaller than the object

Many vehicle side mirrors are convex mirrors. Because images in these mirrors are smaller than the actual objects, they look like they are farther away than they really are. Using a Convex Mirror: 1.The image is always smaller than the object 2.The image is never inverted (it is right side up) 3.The image is always behind the mirror inside the focal point 4.The image is always a virtual image The image is smaller than the object

For that reason, many vehicle side mirrors have the warning, objects in the mirror are closer than they appear, printed on the surface. Using a Convex Mirror: 1.The image is always smaller than the object 2.The image is never inverted (it is right side up) 3.The image is always behind the mirror inside the focal point 4.The image is always a virtual image The image is smaller than the object Objects in the mirror are closer than they appear

Notice that the image in this example is right side up, not inverted. Using a Convex Mirror: 1.The image is always smaller than the object 2.The image is never inverted (it is right side up) 3.The image is always behind the mirror inside the focal point 4.The image is always a virtual image The image is right side up, not inverted

In fact, all images in a convex mirror are right side up. They are never inverted. Using a Convex Mirror: 1.The image is always smaller than the object 2.The image is never inverted (it is right side up) 3.The image is always behind the mirror inside the focal point 4.The image is always a virtual image The image is right side up, not inverted

Notice the image in this case appears to be behind the mirror Using a Convex Mirror: 1.The image is always smaller than the object 2.The image is never inverted (it is right side up) 3.The image is always behind the mirror inside the focal point 4.The image is always a virtual image The image is behind the mirror

It turns out that in a convex mirror, the image always appears to be behind the mirror. Using a Convex Mirror: 1.The image is always smaller than the object 2.The image is never inverted (it is right side up) 3.The image is always behind the mirror 4.The image is always a virtual image The image is behind the mirror

Notice that the image here is formed by dotted lines crossing, not by real solid rays. Using a Convex Mirror: 1.The image is always smaller than the object 2.The image is never inverted (it is right side up) 3.The image is always behind the mirror 4.The image is always a virtual image No solid rays cross to form the image, only dotted lines

This means that the image is a virtual image. Using a Convex Mirror: 1.The image is always smaller than the object 2.The image is never inverted (it is right side up) 3.The image is always behind the mirror 4.The image is always a virtual image No solid rays cross to form the image, only dotted lines A Virtual Image

In fact, all images in convex mirrors are virtual images. Using a Convex Mirror: 1.The image is always smaller than the object 2.The image is never inverted (it is right side up) 3.The image is always behind the mirror 4.The image is always a virtual image No solid rays cross to form the image, only dotted lines A Virtual Image

In review, these four descriptions are true for all images formed by a convex mirror. Using a Convex Mirror: 1.The image is always smaller than the object 2.The image is never inverted (it is right side up) 3.The image is always behind the mirror 4.The image is always a virtual image

The image is always smaller than the object Using a Convex Mirror: 1.The image is always smaller than the object 2.The image is never inverted (it is right side up) 3.The image is always behind the mirror 4.The image is always a virtual image

It is always right side up, Using a Convex Mirror: 1.The image is always smaller than the object 2.The image is never inverted (it is right side up) 3.The image is always behind the mirror 4.The image is always a virtual image

It is always behind the mirror Using a Convex Mirror: 1.The image is always smaller than the object 2.The image is never inverted (it is right side up) 3.The image is always behind the mirror 4.The image is always a virtual image

And its always a virtual, rather than real image. Using a Convex Mirror: 1.The image is always smaller than the object 2.The image is never inverted (it is right side up) 3.The image is always behind the mirror 4.The image is always a virtual image

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