Calculations with wavelength and frequency

Key Questions

  • How can I calculate wavelength given frequency?

    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"))

    Truong-Son N. · 2 · Nov 15 2015

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