Vibrating hot air around heater The other day I was in a restaurant and I saw one of those patio heaters that looks like lamps turned on. The air around it appeared to be vibrating. Why does this happen from the optics point of view? (couldn't find a good picture of this) 
 A: It seems that the term you are looking for is "heat haze" https://en.wikipedia.org/wiki/Mirage#Heat_haze
A: When air is heated up, but the pressure is constant, the density will decrease (in accordance with the ideal gas law).
Now we usually think of air as having a refractive index of 1.0 - same as vacuum. In fact, the value of the refractive index for dry air at STP is around 1.000277 (at 600 nm).
When you increase the temperature, the refractive index will drop. This in turn means that light that travels through a region that is hotter in some parts and cooler (denser) in other parts will experience a small amount of deflection - whenever the thermal gradient is not parallel to the line of sight.
The normal visual acuity is around 1 minute of arc - that is 1/60th of a degree. This means that light needs to bend just a tiny bit for the eye to notice the deflection. And it turns out that the turbulent flow of hot air contains plenty of refractive index changes.
I believe this is the kind of picture you have in mind (part of a picture of an Airbus 319

It shows that the picture behind the jet engine exhaust is distorted.
