I Reverse engineering refraction

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 ?
upload_2019-3-10_16-39-25.png
 

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BvU

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Hello Gabriel, ##\qquad## :welcome: ##\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 ....
 
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

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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

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

Thanks BvU!
 
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