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Here’s a nice picture I took a couple of years ago at Auckland Airport, looking over Manukau Harbour. Can you work out what’s happened to the Waitakere Ranges?

subrefraction2_reduced.jpg 

I’m in the middle of teaching a group of 3rd years about some of the ways that light doesn’t travel in straight lines, as part of their unit on computer modelling of electromagnetic effects.  It’s interesting that we teach them another paper (a whole 20 points) on electromagnetic waves, but implicitly assume that everything happens either in a vacuum, or in materials that have uniform properties.  In practice, that doesn’t happen.  Air isn’t at all homogeneous, its density, and therefore refractive index, changes significantly with height, and as a consequence, electromagnetic waves (e.g. light, radar, infra-red) don’t travel in straight lines.  Light gives mirages, and sometimes false images suspended upside down in mid-air, radio waves can ‘duct’ (follow the curve of the earth for long distances). Very different from the boring straight-line vacuum propagation (I’m ignoring General Relativity here).   

Next time you’re at the beach, have a look at the horizon for some of these freakish effects.