Fresnel reflection at normal incidence

A Fresnel reflection normal-incidence calculator turns two refractive indices into the fraction of light power reflected when a ray hits a planar dielectric interface head-on. Enter n1 for the incident medium and n2 for the second medium; the tool returns the amplitude reflection coefficient r equals (n1 minus n2) over (n1 plus n2), the power reflectance R equals r squared, the complementary transmittance T equals one minus R, percent forms of both, a clear formula string, substitution steps, and a short message that states the optical result.

What Fresnel reflectance means at normal incidence

When a plane electromagnetic wave strikes a planar interface between two homogeneous isotropic dielectrics, part of the optical power is reflected and part is transmitted. The amplitude of each polarization component depends on the angle of incidence and on the refractive indices of the two media through the Fresnel equations. At normal incidence the angle is zero, the plane of incidence is undefined, and the s and p amplitude coefficients collapse to the same simple ratio: r equals (n1 minus n2) divided by (n1 plus n2).

The power reflectance is then the square of that amplitude, R equals r squared, which expands to ((n1 minus n2) over (n1 plus n2)) squared. For non-absorbing media the power transmittance at normal incidence is T equals one minus R, equivalently four n1 n2 over (n1 plus n2) squared. Classic classroom checks use air to glass: n1 near one and n2 near one point five, which yields R near four percent—the familiar four-percent single-surface reflection that anti-reflection coatings try to suppress.

When the indices are equal, r and R vanish and all power is transmitted; when the interface is reversed (glass to air), R is the same because the squared ratio is even in the index difference, while the signed amplitude r flips sign. Teachers care about the non-positive-index rejection as much as the arithmetic: a student who plugs n equals zero or a negative placeholder has left the physical domain of this tool, and a silent NaN or absolute-value fallback would hide that mistake.

The check path recomputes ((n1 minus n2) over (n1 plus n2)) squared with the same fixed rounding used for published fields, so a successful response always ships with steps you can assert in tests or worksheets.

Practical tips, limits, and related searches

Use the refractive indices at the wavelength of interest when dispersion matters: glass and plastics change n across the visible band, so a single n pair is a monochromatic approximation. Keep both indices inside the published positive range so the denominator cannot collapse and the reflectance cannot overflow into a non-finite value that the solver must reject. Prefer sending numbers rather than pre-formatted strings when you control the client; string numbers are accepted only when they match a strict finite numeric pattern.

Prefer this capability when you already have two positive indices and only need the head-on single-surface R and T; if your source is a material datasheet with n at several wavelengths, pick the row that matches your laser or LED first. Round-trip checks are easy: recompute ((n1 minus n2) over (n1 plus n2)) squared by hand or in a calculator and confirm it equals reflectance within the same twelve-decimal rounding, then verify transmittance equals one minus R.