When thinking about how the WiFi signal propagates through a household, can I use the following thought experiment?
Assume absolute darkness. Place a strong lightbulb where the WiFi access point is. The illumination that reaches various places in the house is approximately proportional to the strength of the WiFi signal in that place.
How precise is this mental image? I know that the radio waves can penetrate some objects / walls that the light cannot. Is this at least somewhat representative?
It's more like the walls were semi-transparent glass, if you want to imagine it as light (and even then, you neglect diffraction effects). It would actually be better to imagine it as sound!
But this seems to be exactly what you're looking for:
http://arstechnica.com/gadgets/2014/08/mapping-wi-fi-dead-zones-with-physics-and-gifs/
It's hard to access how 'accurate' an analogy is (i.e. how is this being quantified?). But, I think, there is a simple - better analogy:
WiFi is more like sound in a house. The transmitter is a speaker. If its a good, loud speaker, you will still easily be able to hear it in the next room - through a wall. A few walls inbetween and it gets very faint. Depending on the materials in the walls, opening and/or closing doors may or may not make much of a difference. And there may be odd corners or directions where the sound gets louder, or gets extra soft.
I think your mental picture is pretty close to accurate, as long as you bear a few things in mind:
First, the wavelength of the wireless signals are much longer than visible light. At 2.4GHz, the wavelength is 12.5cm. Just imagine that the waves are about half a foot long (if you have 5GHz wireless, the waves are half as long). So you can get some phenomenon you don't really see with normal light but you've probably perceived with sound; dead zones where the signal is really weak or totally nonexistent.
Second, the opaqueness/transparentness of a material is dependent on the wavelength of the EM waves. The common dielectric structural elements of the house (drywall, furniture, etc) would bend the light to varying degrees (as a function of dielectric constant), as well as absorb/scatter the "light". Steel ibeams and any other metal elements would appear like really shiny surfaces, especially if they are significant fractions of the wavelength; these objects would cast "shadows" and create a lot of scattering and dead zones. A half-foot long wire matching the polarization of your wireless antenna would reflect brilliantly, but some small staples scattered on your desk would only scatter the light a bit.
So imagine a semi-transparent house with all the metal parts being jet-black until any incident radiation hits it, with most of the light bouncing off (less shiny if it's full of iron, more shiny if it's gold/silver). Then imagine pockets of extra brightness and extra darkness as a result of the interference patterns that will inevitably appear. If you switch out your handy 2.4Ghz "lightbulb" isotropic antenna with your 5GHz one, the interference patterns will be different sizes/locations. You'd also have to adjust the way you see everything; the transparent-ness of everything in the house will be different at a different frequency, with some things getting hazier and other things being more clear.
Hardware hacker CNLohr did a nice time lapse collection of signal strength mapping a 4 foot square in his house, and then a 3d cube with the help of a CNC router table. I saw it on hackaday, his project is here: https://hackaday.io/project/4329-wifi-power-mapping
And he links to a cool video here: https://www.youtube.com/watch?v=aqqEYz38ens
It pretty much verifies the arstechnica map from @orion, giving proof that sometimes your notebook has great reception on one part of a desk but move it an inch and the wifi signal can mysteriously vanish. It's like a waveform but bounces in two planes in 3d space causing good spots where the signal can get to the antenna and others where the signals are absorbed or reflected out of the way back to the receiver.
