Question

How can I calculate wavelength given frequency?

Answer 1

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"))`