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You measure the frequency and get to a 'photon energy'. Planck's 'black body' is a experimental proof of light having a wave/particle duality that you can use for measuring a 'photons' energy, extended by Einsteins 'photoelectric effect' . http://spiff.rit.edu/classes/phys314/lectures/photoe/photoe.html
E = hf = hc/λ by definition.
it seems to me that none of these arguments involve directly measuring the energy E in joules of a single photon as per the E=hf equation.
That is correct. There is no good way to directly measure the energy of a single photon.
But, if you go back and look at the answers that were given to you, you will see that we can transfer the energy from photons to electrons, and then measure the energy of the electron. We can do tests to make sure that each electron is only absorbing the energy from a single photon, and we can do tests to make sure that all of the energy from the photon goes to the electron. And we can do tests to measure the wavelength of the photons. Therefore, we can indirectly get very accurate measurements of the energy that a photon has as a function of wavelength.
Since the double slit diffraction experiment works with a single photon, and the diffraction pattern depends on the photon wavelength, it is a direct measure of λ for a single photon
I just have a quibble with the suggestion that the double slit experiment can directly measure the wavelength λ for a single photon.- The probability that the photon will strike a particular place on the screen is certainly a function of wavelength- But the probability is non-zero for a wide range of positions and a wide range of wavelengths- So the fact that a single photon strikes a particular point on the screen cannot distinguish (say) λ from 1.5λ- In particular, the maximum and minimum probability for λ is also a maximum and minimum for λ/2 (when the angle is small)
Except that "duality" is not modern thinking!