Snell’s law — refraction at a plane interface (optics/electromagnetics) A plane wave traveling in medium 1 (refractive index n1) strikes a plane boundary with medium 2 (refractive index n2) at incidence angle θi. Which relation correctly gives the refraction angle θr in medium 2?

Introduction / Context:
Refraction describes the change in direction of a wave as it passes between media of different optical densities. Snell’s law quantifies this change using refractive indices and the angles measured from the normal to the interface.

Given Data / Assumptions:

• Homogeneous, isotropic, lossless media with refractive indices n1 and n2.
• Angles θi and θr are measured from the interface normal.
• Planar boundary, no surface relief.

Concept / Approach:

Snell’s law arises from phase matching of the tangential wave number across the boundary. The classical form is n1 * sin θi = n2 * sin θr, which can be rearranged to sin θr = (n1 / n2) * sin θi. Equality of incidence and refraction angles (θi = θr) is false except when n1 = n2 or at normal incidence.

Step-by-Step Solution:

Verification / Alternative check:

Special cases: normal incidence (θi = 0) gives θr = 0. If n2 > n1, θr < θi; if n2 < n1, θr > θi. Total internal reflection occurs when (n1 > n2) and θi > θc where sin θc = n2/n1.

Why Other Options Are Wrong:

• (a) violates Snell’s law unless n1 = n2 or θi = 0.
• (e) contradicts the empirically verified and theoretically derived law.

Common Pitfalls:

• Measuring angles from the interface instead of the normal.
• Confusing refractive index ratio with its reciprocal in rearranged forms.

Final Answer:

Both (b) and (c) are equivalent statements of Snell’s law.