[Mentor's note: this thread does not use the normal homework forum template because it was originally posted in a non-homework forum, then moved here.] A light beam is incident on a sphere with refractive index n=√3 at an angle i from air and emerges parallel to the horizontal axis passing through the center of the sphere. Find i? Here I made a line from the center of the sphere to the exit point of the ray after which it becomes parallel to the axis. I attached a rough diagram I made in paint for it. Now the triangle formed inside the circle is isosceles and hence two sides and corresponding angles are equal so we have two sides as r and I named the last side as d and the angle at the center is unknown. Here I only have one numerical value (n=√3) and I have to find the angle of incidence. I know there is some geometry involved so I used the cosine rule to solve for the refracted angle but even combined with snells law and other properties of triangles (S and Δ) I just don't see how to proceed, can you guys please help me out?