ho do you find the wavelength of light without knowing the frequency?

Question

anonymous · Answer

I presume that this has to do with refractive indices, related to your previous question.  When light enters into a refractive medium (such as glass) its speed will slow down, but the frequency of the light remains the same.  This means that the wavelength will be shortened in a proportionate manner.  So if you recall that $$n=c/v$$, and if we say that $c=f\lambda_{1}$ and $v=f\lambda_{2}$, then we can worrk out the wavelength by $$n=\frac{f\lambda_{1}}{f\lambda_{2}}$$ or $$n=\frac{\lambda_{1}}{\lambda_{2}}$$.  thus if you know the refractive index, and you know the wavelength of the light in air (or vacuum), then you can calculate the wavelength in the refractive material.

In general $$\frac{n_{2}}{n_{1}}=\frac{v_{1}}{v_{2}}=\frac{\lambda_{1}}{\lambda_{2}}$$ which relates teh speeds wavelengths and refractive indices of any two materials.  Note for vacuum, n = 1, and for air, it is approximately 1 (it is actually 1.00029 at STP).

anonymous · Answer

The other alternative is if you know the energy of the light, then the wavelength can be found using the equation $$E=\frac{hc}{\lambda}$$ where E is the energy, h is Plancks constant, c is the speed of light, and $\lambda$ is the wavelength of the light.  though, I think this may be outside your current topic area, as this is to do with quantum mechanics.