Solar Panel Fresnel Loss (2D): Ray Diagram & Spectral AR Coating

Sun & Panel Geometry

Sun elevation 42°

Panel tilt from horizontal 30°

Glass refractive index 1.52

AR coating design λ 550 nm

Drag the sun or the panel directly in the top diagram to change elevation / tilt.

Live Readouts

Angle of incidence

12.0°

Reflectance R

2.1%

Irradiance on plane

978 W/m²

Electrical output

191.5 W

Reflected away vs. bare glass

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How it works

Only the light that actually enters the glass can reach the silicon underneath. What bounces off the front surface is lost before conversion even begins — this simulator computes exactly how much, from real thin-film optics, not a lookup table.

1. Geometry. For a fixed panel facing the sun's azimuth, the angle of incidence on the glass is the gap between the sun's zenith angle and the panel's tilt:

AOI = |(90° − elevation) − tilt|
Irradiance on plane = 1000 W/m² × cos(AOI)

2. Fresnel reflectance. At each interface, unpolarised light splits into s- and p-polarised components governed by Snell's law (n₀sinθ₀ = n₁sinθ₁):

r_s = (n0 cosθ0 − n1 cosθ1) / (n0 cosθ0 + n1 cosθ1)
r_p = (n1 cosθ0 − n0 cosθ1) / (n1 cosθ0 + n0 cosθ1)

3. Thin-film stack. With the AR coating on, a quarter-wave layer (index n₁ = √n_glass, thickness d = λ_design/4n₁) sits between air and glass. Its reflection combines with the glass interface through the standard two-interface interference formula, evaluated for both polarisations at the true refracted angle inside each layer:

r = (r01 + r12·e^(−2iβ)) / (1 + r01·r12·e^(−2iβ)),  β = 2π n1 d cosθ1 / λ_eval
R = ½(|r_s|² + |r_p|²)

Without a coating this collapses to a single air→glass interface — reflectance near 4% at normal incidence, climbing sharply past ~60° AOI. The live readouts always evaluate R at 550 nm (the peak of the solar spectrum reaching silicon), while the coating's own thickness is built for whatever "design λ" you set — leave it at 550 nm for a perfectly tuned coating, or drag it away to see a real manufacturing detuning show up as extra reflectance even with the coating switched on. The spectral panel (bottom-right) shows why: it plots R across the visible spectrum and marks both the design wavelength and the 550 nm evaluation point.

4. Output. Transmitted power = irradiance × (1 − R); electrical output multiplies that by a fixed 20% module efficiency over a 1 m² panel.

Incoming photons Reflected (lost) Absorbed (converted)

R vs. angle of incidence

R vs. wavelength (at current AOI)