I won't post the entire question here since I would just like a bit of help getting started as I am quite lost. The question is essentially saying that a light ray parallel to the x axis with a wavelength of $\lambda$ is heading into an isosceles triangle with an index of refraction $n_2$ from air with an index of refraction $n_1$. I'm supposed to find the value of $n_1$ so that light of wavelength $>\lambda$ will exit the prism and light of wavelength $<\lambda$ will be reflected perpendicular to the x axis. I am given the value for $n_2$, $\lambda$ and the angles inside the prism.
The main thing I don't understand is how the wavelength is effecting whether or not the light exits the prism. I believe this depends on whether or not the light is experiencing total internal reflection but in this scenario that would be given by $sin\theta _c=\frac{n_2}{n_1}$ I also know that $n=\frac{c}{v}=\frac{c}{f \lambda }\Rightarrow \sin\theta_c=\frac{\lambda_1}{\lambda_2}$ since only wavelength changes in the different mediums. So the the critical angle is clearly affected by the wavelength of light in the different mediums but I just can't figure out how this relates to higher or lower frequencies exiting or staying in the prism.