How to Determine N from Refraction Angles and Constants?

[GabrielCoriiu]

I'm trying to reverse engineer refraction. So given I, R and k in the image, what is N so that sin(θ₁)/sin(θ₂) = k ?

 

[BvU]

Hello Gabriel, $\qquad$ $\qquad$ !
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reverse engineer refraction

Fine, but it would be more sensible to define $\theta_1$ and $\theta_2$ in the conventional manner. The way it looks now makes $\theta_2$ appear completely random to me ...

 

[GabrielCoriiu]

Hi BvU, thank you for the warm welcome. I've changed the image in the original post, I hope this makes it more clear :)

 

[BvU]

what is N

$\vec N$ is the normal vector. It doesn't occur as a vector in Snellius' law.

However, I think I do not understand your question.

 

[GabrielCoriiu]

To rephrase the question, what should the surface orientation be, in order for the refracted ray to focus on a specific point, given the light direction and index of refraction.

 

[BvU]

There is no question of focusing: parallel in is parallel out!
Are you asking about finding a given $\ \theta_1 - \theta_2$ ?

 

[GabrielCoriiu]

Hmmm,

I've just realized that cos (θ₁ - θ₂) is I⋅R, supposedly they are unit vectors. I can now get θ₁ and replace it in Snell's law and solve for θ₁, which is exactly what I want

Thanks BvU!