Convert Wavelength to Frequency Worked Example Problem

This example problem demonstrates how to find the frequency of light from the wavelength.

Problem:

The Aurora Borealis is a night display in the Northern latitudes caused by ionizing radiation interacting with the Earth's magnetic field and the upper atmosphere. The distinctive green color is caused by the interaction of the radiation with oxygen and has a wavelength of 5577 Å. What is the frequency of this light?

Solution:

The speed of light, c, is equal to the product of the wavelength, λ, and the frequency, ν.

Therefore

ν = c/λ

ν = 3 x 10⁸ m/sec/(5577 Å x 10^-10 m/1 Å)
ν = 3 x 10⁸ m/sec/(5.577 x 10^-7
ν = 5.38 x 10¹⁴ Hz

Answer:

The frequency of the 5577 Å light is ν = 5.38 x 10¹⁴ Hz.