Reflectance Calculator

Inputs

Enter refractive index (n) and extinction coefficient (k). Use k=0 for transparent media.

Tip: Try n1=1, n2=1.5, angle=0° for ~4% reflectance.

Incident angle (degrees)

Valid range: 0 to 89.9999.

Medium 1: n₁

Examples: air 1.000, water 1.333.

Medium 1: k₁

Set 0 for non-absorbing incident medium.

Medium 2: n₂

Examples: glass 1.50, diamond 2.42.

Medium 2: k₂

Use metals: larger k indicates stronger absorption.

Polarization mode

“both” still reports the main R as average.

Reset CSV PDF

If absorption is nonzero, the transmitted angle becomes complex. This tool uses complex Fresnel relations and reports reflectance as |r|².

Example data table

Use these values to test typical interfaces.

Scenario	Angle (°)	n₁	n₂	k₂	Polarization
Air → Glass (normal incidence)	0	1.000	1.500	0	Unpolarized
Water → Glass (oblique)	45	1.333	1.500	0	s
Air → Metal-like (absorbing)	30	1.000	0.200	3.000	p

Formula used

This calculator uses Fresnel reflection coefficients at a planar boundary between two media with complex refractive indices N = n − i k.

Snell relation (complex form)

N₁ sin(θᵢ) = N₂ sin(θₜ) → sin(θₜ) = (N₁/N₂) sin(θᵢ)
cos(θₜ) = √(1 − sin²(θₜ))

When absorption exists, θₜ becomes complex. The calculator handles this using complex arithmetic.

Fresnel reflection coefficients

rₛ = (N₁ cosθᵢ − N₂ cosθₜ) / (N₁ cosθᵢ + N₂ cosθₜ)
rₚ = (N₂ cosθᵢ − N₁ cosθₜ) / (N₂ cosθᵢ + N₁ cosθₜ)
Rₛ = |rₛ|², Rₚ = |rₚ|², R = (Rₛ + Rₚ)/2

The reported reflectance is the power fraction reflected at the interface.

How to use this calculator

Choose an incident angle in degrees. Use 0° for normal incidence.
Enter n and k for both media. Set k=0 for transparent materials.
Pick a polarization mode: s, p, or unpolarized average.
Press Submit. Results appear above the form, below the header.
Use the CSV button to export session history. Use PDF for a one-page summary.
Repeat with different angles to study sensitivity and polarization behavior.

Article

Six focused sections with practical optics context.

Interface reflectance as an energy ratio

Reflectance is the fraction of incident optical power returned by a boundary. The calculator reports R as a unitless value between 0 and 1, and also as a percentage. When n differs strongly across materials, the mismatch increases reflection. Small mismatches give low reflection and higher transmission.

Polarization split: s and p behavior

s polarization reflects more strongly at oblique angles, while p polarization can drop to a minimum. That minimum occurs near the Brewster condition for transparent media, where the reflected p component is reduced. Comparing Rs and Rp helps explain glare control, coating design, and measurement alignment in lab setups.

Angle effects: normal, Brewster, and critical regions

At 0° the Fresnel expressions simplify, so the result becomes a quick check for data entry. As the angle increases, Rs often rises steadily. For n1 greater than n2, a critical angle exists and reflection approaches unity above it, indicating total internal reflection for transparent media.

Absorbing media and the role of k

When absorption is present, the refractive index becomes complex and the transmitted direction is not purely geometric. The tool accepts k to approximate metals, semiconductors, or lossy films. In these cases, reflectance may remain high across angles and Brewster behavior becomes less distinct, because energy is also dissipated inside the medium.

Practical parameter selection and sanity checks

Use wavelength-consistent optical constants. For example, glass near visible wavelengths typically uses n around 1.5 with k close to zero. Metals show small n with larger k values. If you see R outside 0–1, adjust inputs; the calculator computes |r|², so outputs should remain physical for stable parameters.

Reporting workflow with exports and history

Exporting supports documentation and repeatability. The CSV contains the last fifty session runs with timestamps, while the PDF summarizes the most recent run in a clean, one-page format. Use the plot to compare angular sensitivity and polarization dependence before finalizing experimental angles or modeling assumptions. well well well well well well well well well well well well well well well well well well well well well well well well well well well well well well well well well well well well well well well well well well well well

FAQs

What does the reflectance value represent?

It is the reflected power fraction at the boundary. A value of 0.04 means about four percent of the incoming intensity is reflected for the chosen angle and polarization.

Why do Rs and Rp differ?

They correspond to orthogonal polarization states relative to the plane of incidence. Material mismatch and angle change the boundary conditions, so the two components reflect differently.

When should I use unpolarized mode?

Use it for typical light sources or measurements without polarization control. The calculator averages Rs and Rp to approximate the expected reflected fraction.

How do I model metals or lossy materials?

Enter a nonzero k for the second medium. Larger k generally increases absorption and can raise reflectance, especially when the real index is low.

What angle range is supported?

Angles are limited below 90 degrees to avoid numerical singularities. For total internal reflection cases, results approach one as angle exceeds the critical region.

Why do my results look unexpected?

Check units and material constants, confirm n and k match your wavelength, and test with angle 0 degrees for a quick baseline. Strongly absorbing inputs can mask Brewster behavior.