If possible, How many combination between the numbers of the different layers and the thickness of each layer will give me 180° refraction.
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$\begingroup$ What are your ideas about an answer to you problem? $\endgroup$– FarcherJan 22, 2017 at 5:34
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$\begingroup$ what type of glass? $\endgroup$– user140434Jan 22, 2017 at 5:37
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$\begingroup$ That looks like 180° not 360° $\endgroup$– John RennieJan 22, 2017 at 6:34
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$\begingroup$ But you get 360 from two sets back to back. White layers on the outside, black on the inside. $\endgroup$– mmesser314Jan 22, 2017 at 7:03
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$\begingroup$ Do you mean to describe a dichroic mirror? That isn't done exactly by refraction, rather by wavelength-dependent multiple reflections. $\endgroup$– Whit3rdJan 22, 2017 at 7:23
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1 Answer
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Yes, what you need is for the light to be totally internally reflected at some point. You can't achieve this just with refraction because refraction can only make the incoming ray parallel to the interface and not bend it back. So you need to reflect the ray at some point. For this you need the incoming angle (angle to the normal) at one of your sheet boundaries to be greater than the critical angle:
$$ \theta_i \gt \arcsin\left(\frac{n_2}{n_1}\right) $$
So you need to choose the upper sheets to deflect the light ray towards the horizontal, i.e. to increase the incoming angle, then one last sheet to totally internally refract it.
However note that you still can't achieve a complete 180° turnaround. That's because if the incoming light is exactly normal to your sheets of glass it won't be refracted at all. You need the incoming angle of incidence to be great than zero, and that means the outgoing angle will also be greater than zero. Your turnaround will always be less than 180°.
answered Jan 22, 2017 at 7:25