The steps are pretty simple, Jessica. theta1 is the angle of incidence of alight wave as it approaches a barrier between two mediums with different indexes of refraction(n1 and n2). Theta 2 is the angle of reflection.
So, a light wave approaches travelling along theta one througn1, crosses the line and is reflected into n2 at a different angle.
So, n1(sin theta 1) = n2(sin theta 2) - divide both sides by n2
Sin (theta2) = n1 (sin(theta1) / n2
So, theta2 = sin^-1 (sin theta1)* n2/n1