Answer:
We want to make the beam to refract less as it exits the prism, so we want to increase the internal reflection inside the prism.
We could do this by approaching the critical angle of incidence when the beam wants to leave the prism, this is:
By using snell law:
n1*sen(a1) = n2*sen(a2)
Here n1 is the material of the prism and n2 is air, so we can suppose that n1 >n2
And a1 and a2 are the angles of incidence and refraction.
so we have that:
sen(a1) = (n2/n1)sen(a2)
Now, the max value of the left side is smaller than 1, so if we take sen(a2) = 1 (this means that the refracted beam is tangential to the wall of the prism, so there is no refracted beam after this angle) then we have:
Sen(a1) = n2/n1
a1 = asin(n2/n1) is the critical angle, and for angles bigger than that there is total internal reflection.
So approaching this angle is a good way to reduce the "amount" of the beam that is refracted when it exits the prism.
