"Objects in the mirror are ..." actually images in the mirror

Have you ever looked at yourself in the mirror and imagined that there is a whole other world on the other side of the glass with another version of you? Did you know that there is a whole “virtual” world on the other side of a mirror?

Plane mirrors

Let’s say you have a toy car, and it’s sitting in front of a regular bathroom mirror. The distance between the car and mirror is called the object distance, and it’s always positive. If you look at the image of the toy car in the mirror, it will appear to be the same distance behind the mirror as the real car is in front of the mirror, at the same height. It will also appear to be the same size as the real car. The image of the car looks like it’s behind the mirror (and the light we see does not directly emerge from the image), we say that the image is upright and virtual, and that the image distance is negative.
Viewer and car on one side of the mirror, virtual car on the other side of the mirror with rays traced; dotted on virtual side

Spherical convex mirrors

Convex mirrors that are shaped like part of a sphere or circle, just like plane mirrors, always have a virtual image: the image always looks like it is on the other side of the mirror, and the image distance is always negative. Light rays that come towards the mirror from far away are essentially parallel, but when they hit the mirror they are reflected in all directions. However, there is a virtual focal point on the other side of the mirror if we follow them back into the mirror. The whole setup looks something like this:
Convex mirror with parallel light rays being reflected to a virtual focus
In the sketch, we’ve marked the the location where the light rays converge as the focal point, and we’ve indicated that it is not the same location as the center of the circular mirror. We can see that light rays that come from far away, after being reflected, will look like they are coming from the virtual focal point behind the mirror. We can use this focal point to find out what the image of a reflected object would look like.
The toy car's image is smaller than the actual toy car and is infront of the object (the toy car).
The image is virtual, since it’s behind the mirror, and it is upright.

Spherical concave mirrors

Like spherical convex mirrors, spherical concave mirrors have a focus. If the object is closer to the mirror than the focal point is, the image will be virtual, like we talked about before for the plane mirror and the convex mirror.
The image of the object (the toy car) is larger.
Concave mirrors, on the other hand, can have real images. If the object is further away from the mirror than the focal point, the image will be upside-down and real---meaning that the image appears on the same side of the mirror as the object.
The toy car image is smaller and inverted when using a concave mirror.
The closer the object comes to the focal point (without passing it), the bigger the image will be.
You can try this yourself by looking into the concave side of a shiny spoon. If you look into the spoon while holding it at arm’s length, you’ll see an extremely magnified, upside-down image of your face. But as you bring the spoon closer to your eyes, the image will get bigger and bigger.

Consider the following… car mirrors

Traffic mirrors to help see around corners at intersections use convex mirrors so that the image will always be virtual and upright, but smaller than the actual scene, so that you can see more of the road than you otherwise would be able to. But a side effect of this expanded field of view is that the virtual distances are compressed, hence the origin of the ubiquitous phrase “objects in the mirror are closer than they appear.”
This article is licensed under a CC-BY-NC-SA 4.0 license. https://creativecommons.org/licenses/by-nc-sa/4.0/
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