State Snell's law for refraction in terms of media with refractive indices n1 and n2 and incidence and refraction angles θ1 and θ2.

State Snell's law for refraction in terms of media with refractive indices n1 and n2 and incidence and refraction angles θ1 and θ2.

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

Answer: (C)

When light crosses a boundary between two media, the quantity that must stay consistent is the component of the wave’s propagation parallel to the boundary. This requirement leads to the relation n1 sin θ1 = n2 sin θ2. It comes from the fact that the tangential component of the wavevector (k) is continuous across the boundary, and since k is proportional to the refractive index n (k = nω/c), the sine factors pick up the n’s on each side, giving this law. Intuitively, the refractive index tells us how much the light slows down in a medium (n = c/v). When light enters a medium with a larger n, it slows down more and bends toward the normal, which is consistent with n1 sin θ1 = n2 sin θ2. You can also rewrite this relation as sin θ1 / sin θ2 = n2 / n1, which is the same condition written in a different form. The form with a cosine would mix up the geometric projection and is not the correct way to express how the boundary preserves the tangential component of the wave’s propagation. The version that would force θ1 = θ2 regardless of the media is also incorrect, since refraction fundamentally changes the direction unless the indices are equal.

When light crosses a boundary between two media, the quantity that must stay consistent is the component of the wave’s propagation parallel to the boundary. This requirement leads to the relation n1 sin θ1 = n2 sin θ2. It comes from the fact that the tangential component of the wavevector (k) is continuous across the boundary, and since k is proportional to the refractive index n (k = nω/c), the sine factors pick up the n’s on each side, giving this law.

Intuitively, the refractive index tells us how much the light slows down in a medium (n = c/v). When light enters a medium with a larger n, it slows down more and bends toward the normal, which is consistent with n1 sin θ1 = n2 sin θ2.

You can also rewrite this relation as sin θ1 / sin θ2 = n2 / n1, which is the same condition written in a different form. The form with a cosine would mix up the geometric projection and is not the correct way to express how the boundary preserves the tangential component of the wave’s propagation. The version that would force θ1 = θ2 regardless of the media is also incorrect, since refraction fundamentally changes the direction unless the indices are equal.