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So I have a high school physics project and I essentially have this experiment idea where I use spectroscopy to find the surface temperature of the sun. Now I'm essentially going to assume the Sun is a black body, then using a spectroscope I can analyse the spectra of the sun light and hence determine the peak wavelength. My idea is to then utilise Wien's Displacement Law to find the temperature of the sun. Now I'm not sure if this would work and was wondering if it does.

This is high school physics so I'm probably making a lot of assumptions here that may be inaccurate, but if the experiment gives me a temperature value that is close to the actual value that would be fine. Also our spectrometers aren't very advanced. It basically displays the spectra on a screen and then to analyse it my teacher's have told me that I would need to take a photo of the spectra and utilise software to create a wavelength vs intensity graph of the spectra. Then use that to find the peak wavelength.

Anyhow any advice around wether this experiment would work, limitations and improvements would be greatly appreciated.

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    $\begingroup$ Google a blackbody spectrum for 5000K and then google "Solar irradiance curve". Then compare them and judge for yourself. $\endgroup$
    – DKNguyen
    Commented Apr 28, 2023 at 4:09
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    $\begingroup$ en.wikipedia.org/wiki/… $\endgroup$
    – anna v
    Commented Apr 28, 2023 at 13:46
  • $\begingroup$ I think this is a great experiment! And one that should be accessible if you have a working spectrometer. I didn't really learn about optical spectra, much less use a spectrometer, until graduate school. So I commend your physics teacher for this. $\endgroup$
    – RC_23
    Commented Jun 3 at 5:29

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Yes it will work to some extent.

Theoretically, the problem is that the Sun isn't a perfect blackbody - the usual "effective temperature" quoted for the Sun is the temperature of an ideal blackbody of the same radius as the Sun that would produce the Sun's luminosity. This is a little different to the temperature you would get from measuring the wavelength where the Sun's spectrum peaks, but not by more than a few hundred Kelvin.

Practically, you will need a way of compensating for the wavelength response of your spectrograph and detector. Their optical properties and sensitivity to different wavelengths could shift the peak from where it should be. A way of calibrating this could be to observe a blackbody source of known or estimated temperature (e.g. a tungsten lamp) and assume that this has a blackbody spectrum (the Rayleigh Jeans tail) at visible wavelengths.

A second problem is compensating for atmospheric absorption. Blue light is preferentially absorbed/scattered, which shifts the peak of the observed blackbody to the red. This is probably not a huge effect and could be corrected using a theoretical atmospheric extinction curve.

Finally, you have to make sure your wavelength axis is calibrated and linear. i.e. Each pixel in your spectrum plot should correspond to an equal wavelength interval. If the axis is non-linear it could shift where the peak of the spectrum is observed.

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