It is not because the air is hot it is because it is warmer than the surrounding air.
The first part is warm air is less dense the cooler air so it rises. It will not rise in a perfectly smooth, there is always wind and turbulence, Look at how frames in an outdoor fire behave.
The second part is the index of refraction of warm air is different from cooler air. If light passes between medium with different indexes of refraction its direction changes.
This is why if you put a straight stick into the water and look at it from above it does not look straight. This is also how lenses work.
The difference in the index of refraction is less between cold and warm air compared to air and glass or water so the amount the light gets bent is lower.
Home muck the light bend depends on the different index of refraction and the angle between the light and the surface between the two materials.
The rising warmer air will not have a smooth surface or really a surface at all it will be a gradient but let’s ignore that. Think instead of rising warm air as something similar to water where the surface moves amount but vertically. Then let’s look at the reflected sky instead of what is below the water it is often simpler to see. If you have water where the surface moves the reflected sky will be wobbly, If you are in a pool and look out through the surface what you see is wobbly.
The effect will be more pronounced for water than how air but the phenomena is the same. the light passes through material with different indices of reaction that change the shape all the time and light will be bent in a nonuniform way ie it wobbles.
You can see the sky reflected in the air too like the water. You need to look with a low angle relative to the “surface” of the hot air and there has to bee a high-temperature difference. You get that if you for example look along a hot road like https://qph.cf2.quoracdn.net/main-qimg-68be869c597075a0f14feb78512048ae-lq
Light bends when you look through a glass of water. It does this because the path light takes changes when it moves between materials with different densities. Hot air and cold air have different densities too, and so when you see a place where hot air and cold air are mixing together, light will get wobbly because the density of air right in that spot is wobbly.
Even though things are transparent light still travels differently through deffrent transparent mediums. This is how you can see the difference between a empty glass and a glass full of water. This is called refraction. The index of refraction is affected by things like temperature so when hot air mixes with cold air you will see the boundaries between the two as the light passes through them differently.
There are many correct answers, but they don’t quite hit the nail on the head.
Although hot air has a different density, that’s not what causes this effect. There are many gases (and some liquids) that have a different density to air but the same refractive index.
Hot air, on the other hand, has a different refractive index to cool air, which means that if we look through it, the light bends in a different way.
Have you seen that experiment where the arrow changes direction when the glass of water is in front of it? The same thing is happening, although to a lesser extent, when we see warm air rising from a hot surface. We need a lot more than just a glass, and the hot and cold air needs to be close together for it to be noticeable.
What about 2d? Take a clear shower curtain put it on the road. Now get 6-8 you’ve never met to help lift it top to bottom. 1 person each at top corners and start lifting. No one knows what they’re doing the curtain doesn’t rise flat and clear. You’ll see all the wrinkles because left bottom corner is pulling up too fast right bottom corner is kind of swishing it around back and forth while raising it up the other four to whatever have no idea and I’m just kind of pulling it around in the middle and up and now you’re seeing all those wrinkles. I don’t know I tried
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