Convex Mirror

Move the object near and far, and keep an eye on how big its image is.

Upright and much smaller, behind the mirror, seen by looking into it. Like a car’s side mirror.

Object distance: 26 cm
Image distance: 7.2 cm behind
Size: 0.28 × upright

Focal length: 10 cm (a mirror that bulges more has a shorter focal length)

What’s happening

Look at yourself in the back of a spoon: you are small and upright, with the whole room squeezed in around you. A convex mirror bulges outwards like that. Each part of the bulge faces a slightly different way, so together they catch light from a very wide view, much wider than a flat mirror of the same size. The light it reflects spreads apart and never comes together; your eye follows it back to a small, upright image behind the mirror, never further back than the focus F.

Try this

Can you make the image as big as the object? How close do you have to get?
Drag the object far away. Does the image ever pass F?
Make the mirror bulge more. Does the image get smaller or bigger?
Which way up is the image? Can you turn it over anywhere?
At home: look into a shiny ball or a steel bowl turned upside down. How much of the room can you see in it?

Learn more: the three rays, why it shows so much, and mirrors on mountain bends

The three rays work for a mirror that bulges too, only they leave spreading apart:

Parallel ray: comes in parallel to the axis, and reflects as if it came from the focus behind the mirror.
Middle ray: hits the middle of the mirror, and bounces off at the same angle on the other side of the axis.
Focal ray: heads for the focus behind the mirror, and reflects parallel to the axis.

The mirror equation is the same as for a concave mirror, where $u$ is the object distance, $v$ the image distance and $f$ the focal length:

\frac{1}{f} = \frac{1}{u} + \frac{1}{v}

but a convex mirror’s focus is behind it, so its focal length counts as negative: half the radius $R$ of the ball its curve would make, with a minus sign.

f = -\frac{R}{2}

Then the image distance $v$ always comes out negative too: the image is behind the mirror, a virtual one. And its size is always between 0 and 1, upright and smaller:

m = -\frac{v}{u}

Side mirrors on cars and motorbikes: they show the whole road behind. Some carry the words “Objects in mirror are closer than they appear”, because the small image makes cars look further away.
Mirrors on mountain road bends: drivers see what is coming round a corner they can’t see past.
Shop security mirrors: one round mirror in a corner shows a whole aisle.

Why the wider view? A flat mirror sends light from only a small patch of the world into your eye. A convex mirror’s edges are tilted outwards, so they catch light from far off to the sides and still send it to you. The price is that everything looks smaller and squeezed together, just like in a wide-angle camera lens.

Convex Mirror

What’s happening

Try this

See it at Science Playground