MadSci Network: Physics Query:

### Re: what percentage of the electromagnetic spectrum is visible light?

Date: Mon Aug 27 17:24:17 2007
Posted By: John Link, Senior Staff Physicist
Area of science: Physics
ID: 1188227546.Ph
Message:

The question: "What percentage of the electromagnetic spectrum is visible light? I've read that visible light makes up a very tiny portion of EM radiation or frequency. I am curious if there is a more precise known percentage of visible light in relation to the whole (the other six wavelengths of the spectrum)."

Let's examine the available information. The electromagnetic spectrum is usually considered to extend from radio waves to gamma rays, with frequencies from about 10000 Hz to 1019 Hz, respectively, while visible light goes from red to violet with frequencies from about 4x1014 Hz to about 7.5x1014 Hz, respectively.

So, if the entire spectrum is taken to span 15 orders of magnitude (log10(1019) = 19, log10(104) = 4, and 19 - 4 = 15) while the visible spectrum spans only 0.35 of an order of magnitude, then we can say that the visible spectrum is 100%*0.35/15 of the entire electromagnetic spectrum, which works out to about 2.3%. But that is on a logarithmic scale, so let's do the calculation again on a linear scale:

The entire spectrum has the range 1019 Hz - 104 Hz, which is 0.999999999999999x1019 Hz. The visible spectrum has the range 3.5x1014 Hz. So 100%*3.5x1014/0.999999999999999x1019 = 0.0035%.

So, on a logarithmic scale of frequency, visible light is 2.3% of the whole electromagnetic spectrum, while on a linear scale it is 0.0035%.

If you would rather do the calculation using wavelengths I think there is enough information here for you to able to do so.

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