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From the camp fire heat is carried into surrounding air by the process of convection.during this process the density of surrounding air changes continuously.thus changes it refractive index slightly. this change in refractive index gives raise to continuous change in angle of refraction which results in objects seeming to be swaying.
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Due to the heat , differences in density in the gases or the air produce refraction..
these differences change from one moment to another in density and so you can see the fire swaying...

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