Question

How do I convert between wavelength and frequency and wavenumber?

Answer 1

Frequency ($\nu$ ) and wavelength ($\lambda$) are joined with the aid of using the equation $\nu \lambda = c$ , in which c is the rate of mild. As the rate of mildness is constant, in case you grow the frequency, the wavelength has to be lower to preserve this equation and vice versa.

Complete answer:
We are considering interchanging among $\lambda$, $\nu$, and $\widetilde \nu$. We recognize that it is usually wavelength in nm, ν is usually frequency in ${s^{ - 1}}$ , and approach strength in wave numbers ($c{m^{ - 1}}$). If you need $n{m^{ - 1}}$, simply reciprocate nm.
There are 4 opportunities for conversions that we ought to cover:
$\lambda$ → $\nu$
$\nu$ → $\widetilde \nu$
$\nu$ → $\lambda$
$\widetilde \nu$ → $\nu$
However, understand that if you may do 1 and a couple of, you've accomplished three and four backwards, and if you may do 1 and a couple consecutively, you may cross directly from λ to (identical with three and four but to ). So, I will most effectively display 1 and a couple of.
$\lambda$ → $\nu$
Suppose we have been given $\lambda$ = $600nm$ for yellow moderate and we want its frequency in ${s^{ - 1}}$.
What we want is to convert from a unit of the period to a unit of reciprocal time, which requires something that has period time units. The tempo of moderation works terrific here, and it's miles approximately$3 \times {10^8}m/s$. Therefore:
Reciprocate the wavelength
Convert to m
Multiply with the aid of using the rate of mild
$\nu$ → $\widetilde \nu$
This reason is straightforward. We have 1s and need 1cm. suppose we've got a frequency of $6 \times {10^{ - 3}}{s^{ - 1}}.$ Divide with the aid of using the rate of mild.

Note:
Convert from wav huge range to wavelength with the useful resource of the use of dividing one with the useful resource of the use of the wave huge range. If the wave huge range is expressed in the inverse of m, you could get a result in m. If the wave huge range is expressed in the inverse of cm, you could get a result in cm.