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I would like to know the physical reasoning behind the fact that temperature indeed does change the index of refraction of a certain medium.

(Is there an easy experiment for me to try this at home?)

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Refractive index does not change because of a change in temperature, it changes because of a change in density. Increased temperature usually reduces density because most materials expand when heated (but some contract). If density is kept the same while temperature changes (eg by varying applied pressure) then there is no change in refractive index.

A simple Science Fair experiment which you could do at home/school is described in the following reports :
http://cssf.usc.edu/History/2008/Projects/J1625.pdf
http://cssf.usc.edu/History/2006/Projects/S1513.pdf
However, these experiments do not make any compensation for the change in density, so it is impossible to tell if the results obtained are due to change in temperature or change in density.

It is difficult to eliminate or compensate for changes in density during the experiment. You could compensate after the experiment by obtaining and plotting data for density of the material at various temperatures within the experimental range and comparing with your measured variation in refractive index. If the two values remain in proportion as temperature varies then you can deduce that the variation is entirely due to density and not at all due to temperature.

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  • $\begingroup$ Thank you, the experiments that you have linked me show change in temperature of a liquid (e.g. water). Let us say I want to see what happens if we change the temperature of surrounding air when performing Young's double slit experiment, would it be ok to heat room to 30 degrees celsius and compare it to the first experiment originally at 16 degreees celsius (using air conditioner)? $\endgroup$ – uioghhenft Dec 16 '17 at 15:29
  • $\begingroup$ Your suggestion would not compensate for change of density of the air, which remains at atmospheric pressure and therefore expands, decreasing its density. You would have to seal the room (or apparatus) air-tight to ensure that air density does not change. $\endgroup$ – sammy gerbil Dec 16 '17 at 15:48
  • $\begingroup$ Oh, you are right. Is that experimentally feasible at home? Do you suggest anyway that I can do this experiment? $\endgroup$ – uioghhenft Dec 16 '17 at 15:58
  • $\begingroup$ The index of refraction at constant density is only (approximately) independent of temperature as long you have no appreciable ionization of the optical medium. At high temperatures air becomes a plasma wit a significantly different index of refraction. $\endgroup$ – freecharly Dec 16 '17 at 16:24
  • $\begingroup$ @uioghhenft No I do not think it is feasible to prevent air from expanding in an "easy" home experiment. You would have to be in a school or university laboratory to do this. ... However, do you really need to keep the density constant? For most practical purposes, it does not make any difference whether the change is due to density or not. It is assumed that pressure is constant, not density. So provided that you keep the (atmospheric) pressure constant, your results will be ok. $\endgroup$ – sammy gerbil Dec 16 '17 at 17:18
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The change of density with temperature is not the only source of temperature dependence of refractive indices. Another cause is the change of polarizability with temperature (at constant density) - http://photonics.intec.ugent.be/education/IVPV/res_handbook/v2ch33.pdf, equation (35)

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