Question

Find the frequency range of visible light, given that it encompasses wavelengths from 380 to 760 nm.

Final Answer

$3.95 \times 10^{14} \textrm{ Hz} \leq f_{visible} \leq 7.89 \times 10^{14} \textrm{ Hz}$

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This is College Physics Answers with Shaun Dychko
We're going to determine the possible range of frequencies for visible light. Now, the wave equation says that the speed of light equals its frequency times its wavelength, and we can divide both sides by

*lambda*to solve for*f*. So the frequency is speed of light divided by the wavelength. The maximum possible frequency will be the speed of light divided by the minimum possible wavelength. So that's three times 10 to the eight meters per second, divided by 380 nanometers, which is times 10 to the minus nine meters. That gives 7.89 times 10 to the 14 Hertz. And then for the minimum frequency, we divide speed of light by the maximum possible wavelength in the visible spectrum. So that's 3 times 10 the 8 meters per second divided by the wavelength of color red, which is 760 times 10 to the minus nine meters. And this gives 3.95 times 10 to the 14 Hertz. And so the frequency for visible light is between these two numbers.