A ray of light hits a side of Lucite ( n = 1.5) prism at 50 degree. Assuming that the nearest vertex has an angle of 70 degrees, what is the angle of light that leaves the prism.

Answer 1

There are two possible 50 degree angles of incidence. They are above and below the normal to the face that the ray strikes. You need to be more specific. Only one of the two 50 degree angles of incidence will strike the opposite face. The other strikes the bottom of the prism

In any case, use Snell's law twice.
The angle of refraction inside the prism is given by

sin A = sin50/1.5 = 0.5107
A = 30.7 degrees

Using a bit of geometry, I conclude that the angle of incidence on the second face is 70 - A = 39.3 degrees.

Apply Snell's law again for the final result.

Answer 2

Wait, how did you do that? I understand the part of 30.7 degree, but how did you conclude that the angle of incidence on the second face is 39.3? Could you show the steps, please?