Polarization at Brewster Angle – Relation between angle and refractive index For a dielectric reflecting surface, the polarizing (Brewster) angle i is related to the refractive index μ of the medium. Which relation holds at the polarizing angle?

Introduction / Context:
When unpolarized light strikes a dielectric surface at a specific angle (Brewster angle), the reflected light is perfectly plane-polarized. This principle is used in glare-reduction photography and in understanding surface reflection behaviour in remote sensing.

Given Data / Assumptions:

• Interface between air (index ≈ 1) and a dielectric with refractive index μ.
• Non-absorbing media; simple geometric optics applies.
• Angle i is measured from the surface normal.

Concept / Approach:

At Brewster angle, the reflected and refracted rays are perpendicular. From Snell’s law and geometry, the tangent of the Brewster angle equals the refractive index of the transmitting medium relative to the incident medium (for air to dielectric, tan i = μ).

Step-by-Step Solution:

Verification / Alternative check:

Measured Brewster angles for glass (μ ≈ 1.5) give i_B ≈ arctan 1.5 ≈ 56–57°, consistent with practice.

Why Other Options Are Wrong:

sin, cos, cot, sec forms do not satisfy the perpendicularity condition derived from Snell’s law at polarization by reflection.

Common Pitfalls:

Confusing Brewster angle with critical angle for total internal reflection; using μ = sin i instead of tan i.

Final Answer:

tan i = μ