Brightness of light and frequency

[dxu425]

Hi all,

I'm hoping someone might be able to clear up a concept issue for me. On the AAMC Assessments Physics section, there's a question that says "As power input to a light bulb decreases, brightness decreases. How does the color of the emitted light change?"

The answer is that the wavelength of the emitted light gets longer, because P = energy/time, so if P decreases, energy decreases, and since E = hc/lamba, lamba must get bigger if E decreases. This all makes sense to me.

However, I thought I had learned in physics that when the brightness of light changes, the only thing that changes is the number of photons that are emitted, and everything else stays constant. That seems contradictory. I know I learned this idea in the context of the photoelectric effect. I'm missing something clearly.

Thanks in advance!

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[milski]

The contradiction comes from the fact that you cannot describe the light completely just by its brightness. While the brightness and the intensity are related, they are two independent properties.

You can say that only for a monochromatic light with a specific wavelength, the brightness (aka intensity) is proportional to the number of photons emitted. For example, if you were bombarding some substance with particles with a fixed energy, all photons coming from that substance will have the same energy and thus the same wavelength.

That's not the case for black body radiation (which is what the light bulb is). Here you have photons being ejected with different amounts of energy. This energy has a normal distribution with an average which depends on the temperature (and the internal energy) of the black body. The total amount of photons ejected also decreases with energy.

For the light bulb, decreased power results in both lower intensity (less photons are being ejected) and lower wave length (each of the photons has less energy).

It can be a bit confusing and that's far from the best explanation, so if anything is unclear, keep asking.