# Critical Value for Dispersion of light [closed]

If there is a ray of light moving from $n_1$ to $n_2$ you can get dispersion if $n_1$ is a function of wavelength. What angle of incidence ($\theta_1$) will maximise the dispersion? My solution so far: Well I looked at Snell's law which is as follows $$n_1sin(\theta_1) = n_2sin(\theta_2)$$ Now we know $n_2=1$ (given in question) and to find maximum dispersion we can say $\theta_2 = \frac{\pi}{2}$ and thus $sin(\theta_2) = 1$. Now our equation becomes $$n_1sin(\theta_1) = 1$$ Now I get a little bit stuck, but what I thought is we know $n_1$ is a function of wavelength and we are trying to find a formula for the critical angle for any wavelength you give me (i.e. that if you give me any wavelength then I can give you a $n_1$ and hence tell you what your critical angle for Total Internal Reflection). I want to try and use the fact that $n=\frac{\lambda}{\lambda_m}$ but then I need to know what the wavelength of light is which can obviously be a range of values. Please can anyone help with this part or give me some tips on how to tackle it?

P.S. I apologise if i explained this poorly but if you are unsure on what I am asking this asking just say so and i will try to explain a different way.

You're simply meant to solve your equation $n_1sin(\theta_1) = 1$ for $\theta_1$ at one wavelength of light. $n_1$ is (assumedly) known at that wavelength, and $\theta_1$ is the unknown critical angle.