Peculiar Mirages & How Topology Helps

Miraged cars in telephoto (300mm) shots by Adam Kraft.

"Today it was 86 degrees and as a passenger I was able to photograph mirages as we traveled along. This particular part of the road is always great for them and I always have my camera ready when we get near it.  The highway has a lot hills and valley's and this is in one of the small valleys."

©Adam Kraft, shown with permission.
About - Submit Optics Picture of the Day Galleries Previous Next Today Subscribe to Features on RSS Feed

What is unusual about this mirage is the car images.   Some are upright!  

We are so used to seeing inverted images in mirages over hot roads where cars and other objects are seemingly reflected in pools of water.    But here there are multiple images of each car some impossible upright, some inverted.

The undulating road is partly responsible by tilting the layers of different temperature air.   Hot road mirages, ‘inferior mirages, are produced by light rays refracted by the temperature gradients between warm air close to the hot solar heated road surface and cooler air above.

While we are used to seeing a single inverted object in road mirages there is no reason why they should be so limited if the mirages is extensive enough and if favourable temperature gradients exist.

We could agonise over the precise temperature conditions and ray paths necessary to produce these multiple car mirages.   But it is not necessary because mathematical topology theory tells us more easily the form that they have to take.

A complete mirage must have an odd number of images if we include the ‘real’ image of the object itself.

The sum of erect images minus the inverted ones must be one.   This severely restricts image orientation, for example three erect images are impossible.

Usually images alternate as erect, inverted, erect A consequence of the rule that a mirage must be capable of being simply deformed by folding or pleating into the real object.

Real life is inevitably richer! Inferior mirages are rarely complete and some images might be so squashed that they are not seen.   Nonetheless, topology theory gives a good guide for what to look for in mirages.