How can I calculate wavelength given frequency?

1 Answer
Truong-Son N.
Nov 15, 2015

If you note the units you are using, it becomes easier.

You have #1/"s"#, and oftentimes with wavelength, you want to convert to #"nm"# which is UV-Vis range (#"200~700 nm"#), and is often of spectral interest.

What you want to do is:

#1/"s" -> 1/"m" -> "m" -> "nm"#

Conversion factors are extremely useful, and one easy one to remember is the speed of light, which is about #"3" xx 10^8 "m/s"#.

#1/(1/cancel("s") * cancel("s")/"m") = "m"#

And finally, we can convert to #"nm"#:

#10^9 "nm" = "1 m" -> "conversion factor: "(10^9 "nm")/("1 m")#

#cancel"m" * (10^9 "nm")/(1 cancel"m")#

Thus, overall, you just have:

#color(blue)("nm") = 1/(1/cancel("s") * cancel("s")/(3xx10^8 cancel"m")) * (10^9 "nm")/(1 cancel"m")#

#= color(blue)(1/(1"/"cancel("s"))*3xx10^8 cancel("m")"/"cancel("s") xx (10^9 "nm")/(1 cancel"m"))#

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