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Brewster angle and the Fresnel reflectance

What you are seeing: light incident on a planar dielectric interface from medium of index n1n_1 onto medium of index n2n_2. The reflectance for ss-polarized light (electric field perpendicular to the plane of incidence) and pp-polarized light (electric field in the plane) follow the Fresnel formulas. The right panel shows Rs(θi)R_s(\theta_i) and Rp(θi)R_p(\theta_i) over the full range of incidence angles. The animated ray sketch on the left shows incoming, reflected, and transmitted beams.

At Brewster's angle θB=arctan(n2/n1)\theta_B = \arctan(n_2 / n_1) the pp-reflectance drops exactly to zero: light at this angle is reflected purely ss-polarized. Polarizing sunglasses exploit this by filtering out ss-polarized glare from horizontal surfaces. If n1>n2n_1 \gt n_2, beyond the critical angle the wave undergoes total internal reflection and both RsR_s and RpR_p equal 1.

Figure 1. Brewster angle and Fresnel reflectance. Method: closed-form Fresnel formulas with Snell's-law refraction.
theta_i56.3 deg
n2 / n11.50
polarizationp
speed2

WHAT TO TRY

  • Vary each control and watch the rail readouts respond.
  • Compare the diagnostic plot against the live scene.