Light Refracted through a Prism

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To determine the largest angle \(\alpha\) for which no light refracts out of a glass prism with a refractive index of 1.66, the discussion emphasizes the application of Snell's Law and the concept of total internal reflection. The angle of incidence at face AC must be calculated to ensure it meets the criteria for total internal reflection. Participants confirm that the incident angle is \(90 - \alpha\) and stress the importance of finding the critical angle for the prism's hypotenuse. The conversation focuses on understanding the relationship between the angles and the refractive indices involved. The goal is to calculate \(\alpha_{max}\) accurately to prevent light from escaping the prism.
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Homework Statement



Light is incident along the normal to face AB of a glass prism of refractive index 1.66, as shown in the figure.

[PLAIN]http://img175.imageshack.us/img175/6339/yffigure3336.jpg

Find \alphamax, the largest value of the angle \alpha such that no light is refracted out of the prism at face AC if the prism is immersed in air.

Homework Equations


I know I'm supposed to use Snells Law, but I really have no idea how to obtain the answer.


The Attempt at a Solution



I know that the incident angle is equal to 90 - \alpha but that's all I know really.

Thanks
 
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Yes the angle of incidence is 90-α
I've drawn it in your diagram. (i)
prism.jpg

You now need to find what angle i needs to be in order that there is total internal reflection at the hypotenuse face of the prism.
Using Snell's Law, do you know the criteria for total internal reflection?
 
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