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We know that blue light has a smaller wavelength and higher frequency than red light, which is a consequence of higher energy in the former, then how is it true that, when scattering light from the sun by a prism, and on measuring the temperatures of the blue and red colours, result shows that the red colour is hotter? If heat is equivalent to energy then William Hershel's experiment contradicts the initial statement.

However, seeing that both statements are scientific truths, the question would then be, what am I missing from the picture?

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    $\begingroup$ Please quote a source. "Hotter" can mean several different things. $\endgroup$ – S. McGrew Nov 12 '18 at 15:43
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    $\begingroup$ Keep in mind that intensity of the light matters as well. $\endgroup$ – Aaron Stevens Nov 12 '18 at 15:46
  • $\begingroup$ A thermometer tells you one thing only: It tells you the temperature of itself. If you replicate Herschell's experiment, and you want to explain the temperature shown on each thermometer, there are a lot of things you have to explain, including, how much power the Sun puts out at different wavelengths, how much of that power makes it through the atmosphere and through the glass of the prism, how well the thermometers are able to absorb energy from the different wavelengths, and the rate at which the thermometers lose heat to the environment when the system is in equilibrium. $\endgroup$ – Solomon Slow Nov 12 '18 at 16:14
  • $\begingroup$ @SolomonSlow but what are you implying? Hershel's experiment is correct yes? $\endgroup$ – user134132523 Nov 12 '18 at 17:10
  • $\begingroup$ I am implying that (a) light does not have a quality called "temperature," (b) the relationship between the temperatures of the different thermometers in the experiment and the color of the light that falls on them probably is more complicated than you assume it to be, and (c), more complicated than I know how to describe (which is why I didn't try to actually answer your question.) $\endgroup$ – Solomon Slow Nov 12 '18 at 17:17
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The energy carried by light is the number of photons per second multiplied by the energy per photon. You are quite correct that blue photons have a higher energy than red photons (by about a factor of two). However in sunlight there are many more red photons than blue photons, so the energy carried by the red light is higher than the energy carried by the blue light. That's why your thermometer gets hotter when placed at the red end of the spectrum.

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