The speed of light, #c#, equals the wavelength, #lambda# (pronounced lambda), times the frequency, #nu#, (pronounced noo).
#c=lambdanu#
#c# is a constant. It is usually given as #3.00xx10^8# m/s or #3.00xx10^10# cm/s rounded to three significant figures.
Wavelength is measured in meters, centimeters, nanometers, etc...).
Frequency has a unit of #"1/s"#, which means #1# cycle per second. It is also given the unit Hertz (Hz) in honor of German physicist Heinrich Hertz who proved the existence of electromagnetic waves. #1 "Hz"="1/s"#.
In order to calculate the wavelength of light, you must know the frequency and the speed of light.
#lambda=c/nu#
Example:
What is the wavelength of light in nanometers (nm) that has a frequency of #5.71xx10^14"Hz"#?
Given/Known:
#c=3.00xx10^8"m/s"#
#nu=5.71xx10^14 "Hz"=5.71xx10^14"1/s"#
Equation:
#c=lambdanu#
Solution: Rearrange the equation given above to isolate wavelength and solve for wavelength.
#lambda=c/nu=(3.00xx10^8"m/s")/(5.71xx10^14"1/s")=5.25xx10^(-7)"m"#
Convert meters to nanometers.
#1"m"=1xx10^9"nm"#
#5.25xx10^(-7)cancel"m"xx(1xx10^9"nm")/(1cancel"m")=525"nm"#
