Which expression represents Snell’s law in terms of refractive indices n1 and n2 for refraction at an interface?

Which expression represents Snell’s law in terms of refractive indices n1 and n2 for refraction at an interface?

• A. n1 sin θ1 = n2 sin θ2
• B. sin θ1 / sin θ2 = n2 / n1
• C. n1 cos θ1 = n2 cos θ2
• D. θ1 = θ2

Answer: (A)

Snell's law links how light bends at a boundary to the optical properties of the two media. The key idea is that the boundary enforces continuity that leads to a simple relationship between the incident angle and the refracted angle through the refractive indices: n1 sin θ1 = n2 sin θ2. This form directly expresses how the product of the index and the sine of the angle remains equal on both sides of the interface, making it easy to solve for either angle if you know the other and the indices. It also shows why the angle changes when light passes into a medium with a different index: the sine term is scaled by the ratio of the indices. An equivalent way to write it is sin θ1 / sin θ2 = n2 / n1, but that is just a rearrangement of the same fundamental relation, with the standard form n1 sin θ1 = n2 sin θ2 being the most conventional.

Snell's law links how light bends at a boundary to the optical properties of the two media. The key idea is that the boundary enforces continuity that leads to a simple relationship between the incident angle and the refracted angle through the refractive indices: n1 sin θ1 = n2 sin θ2. This form directly expresses how the product of the index and the sine of the angle remains equal on both sides of the interface, making it easy to solve for either angle if you know the other and the indices. It also shows why the angle changes when light passes into a medium with a different index: the sine term is scaled by the ratio of the indices. An equivalent way to write it is sin θ1 / sin θ2 = n2 / n1, but that is just a rearrangement of the same fundamental relation, with the standard form n1 sin θ1 = n2 sin θ2 being the most conventional.