A straw in a glass of water looks broken at the surface because light changes direction the instant it changes speed. The rule for how much is Snell's law: $n_1 \sin\theta_1 = n_2 \sin\theta_2$ (read aloud: n-one sine theta-one equals n-two sine theta-two ($\theta$ is the Greek letter theta, the physicist's favourite name for an angle). The subscripts say which side of the border you are on: 1 is the medium the light comes from, 2 the medium it goes into. So $n_1$ and $\theta_1$ are the index and the angle on the way in, $n_2$ the index beyond the surface, and $\theta_2$ — the angle of refraction — is the one these questions solve for. Whatever happens at the boundary, the product $n \sin\theta$ comes out the same on both sides — that is the whole law.

Two habits keep it honest. Every angle is measured from the normal — the line standing straight out of the surface, never the surface itself. And going into a SLOWER medium (bigger $n$), light tips toward the normal. The classic slip waits at the very end: solving gives you $\sin\theta_2$, a plain ratio — the inverse sine (the $\sin^{-1}$ button) is what turns it back into an angle. A sine is not yet an angle; don't let it pose as one.