Calculations with wavelength and frequency
Key Questions
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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.
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2
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Nov 15 2015