Miraged Ships ~ Robert Meldrum looked from Victoria, B.C. across the Strait of Juan de Fuca towards Washington State.

The large ship is a bulk carrier. Its inverted form sails above it. Above that is a third image, this time the right way up. All mirages in their purest form have alternate inverted and erect images.

At left is the Black Ball Line MV Coho, a vehicle ferry on its way from Victoria B.C. to Port Angeles, WA. It too has inverted and erect images sailing above it.

The Strait of Juan de Fuca is famous for its mirages. The ingredients are cold water flowing in from the Pacific Ocean topped by warmer continental air. The lower layer of ocean cooled air forms a temperature inversion. Rays refracted across it form the mirages.

©Robert Meldrum, shown with permission
Rule breaking?

Another of Robert Meldrum's mirages. It's not easy to separate the images but it looks as though the central one(s) disobey the rule that the sequence must always be erect, inverted, erect...

What happens is that the sequence is always there but sometimes the temperature profile causes individual components to be compressed almost into a line (extreme stooping). Equally, others can be vertically stretched (towering).

Rays across an inversion layer - Superior mirages
Ray 'a' from the ship's funnel passes through cold air and is undeviated. But ray 'b' from the same point is refracted downwards to the eye and appears to come from a point higher up. Ray 'c'' from the hull is refracted even more strongly in the gradients between the cold and warm air. It appears to come from higher up still. The result is an inverted image of the ship. More strongly refracted rays form an erect ship image above the inverted one. With the right temperature profile there would be another inverted image above that.

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Rubber Spheres & Mirages - Some Topology

Ray diagrams like the one above say almost nothing in general about miraging. Topology does. It reveals rules governing mirages. What is possible and what is not.

Start by imagining what we see is pasted onto a transparent sphere called an 'image sphere'.

The real object creating the mirage is imagined pasted onto a larger diameter 'object sphere'.

The refractions and curved rays occur between the two spheres but we no longer need to worry about how or why the ray paths get curved.  

Instead we try to transform the mirage on inner sphere into the object on the outer sphere.

We make a copy of the inner sphere called a transfer surface. Then we Inflate it so that it expands towards the outer object sphere. The game is to somehow make the mirage images pasted on the transfer sphere exactly match the single object sphere image. Stretching and folding is allowed, cutting or snipping are not.

Below left: The three mirage images are made to overlay each other and be congruent to the object by folding the transfer sphere twice. If there had been five images then another two folds would have done the trick. Had there been four images it would have been quite impossible.

The point of all this rubbery playing is that it generates deep insights into the underlying rules and structure of mirages. For example, allowed mirages have the sequence erect, inverted, erect,.. Mirages like erect, erect, inverted are not. They cannot be made by smooth folding of the transfer sphere.

Another result is that - in a complete mirage - there are always an odd number of images (including the 'real' one). Try folding the sphere to make an even number! Many mirages are incomplete because the ground or an air layer cuts them off - we do not then see all the images.

For a more complete description see this page.