Optics

Fresnel Reflection (Normal Incidence)

r=n1n2n1+n2,R=r2r = \frac{n_1 - n_2}{n_1 + n_2}, \quad R = r^2

For light at normal incidence, the Fresnel equations simplify to give the reflection coefficient. R gives the fraction of intensity reflected.

Variables

r
Amplitude reflection coefficient
unitless
R
Reflectance (intensity)
unitless
n_1
Refractive index of incident medium
unitless
n_2
Refractive index of transmitted medium
unitless

Derivation

Derived from Maxwell's equations by applying boundary conditions at the interface between two media.

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Common questions

What is the Fresnel Reflection (Normal Incidence) formula?

Fresnel Reflection (Normal Incidence) is written r = n₁ - n₂/n₁ + n₂, quad R = r². For light at normal incidence, the Fresnel equations simplify to give the reflection coefficient. R gives the fraction of intensity reflected. It belongs to Optics, under Reflection.

What are the units in r = n₁ - n₂/n₁ + n₂, quad R = r²?

In SI units, r is amplitude reflection coefficient (dimensionless); R is reflectance (intensity) (dimensionless); n_1 is refractive index of incident medium (dimensionless); n_2 is refractive index of transmitted medium (dimensionless).

How is the Fresnel Reflection (Normal Incidence) formula derived?

Derived from Maxwell's equations by applying boundary conditions at the interface between two media. The result is r = n₁ - n₂/n₁ + n₂, quad R = r².