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Reflection

Feb 09, 20251 min read

Physics

When a wave meets an interface between two mediums of different wave travel speed, reflection of the wave occurs

Topics

Reflection Coefficient
Fresnel’s Equation

$θ_{R} = θ_{I}$

The angle between the reflected light ray and the normal of the surface is equal to the angle between the incident light ray and the normal of the surface

$E_{0_{R}} = \frac{v _{2} - v _{1}}{v _{2} + v _{1}} E_{0_{I}} = \frac{n _{1} - n _{2}}{n _{1} + n _{2}} E_{0_{I}}$

Reflected wave amplitude
$E_{0_{I}}$ is the incident wave amplitude
$v_{1}$ and $v_{2}$ are the wave velocities in medium 1 (from incident wave) and medium 2 (where the incident wave is heading toward)
$n_{1}$ and $n_{2}$ are refraction indices

$δ_{R} = π (v_{1} > v_{2}) + δ_{I}$

Phase difference in reflected wave compared to incident wave is $π$ if the waves travel quicker in the first medium compared to the second, 0 otherwise
I.e. the reflected wave will be upside down relative to the incident wave if waves travel quicker in the first medium

Graph View

Topics
$\theta_R=\theta_I$
$\displaystyle E_{0_{R}}=\left\lvert \frac{v_{2}-v_{1}}{v_{2}+v_{1}} \right\rvert E_{0_{I}}=\left\lvert \frac{n_{1}-n_{2}}{n_{1}+n_{2}} \right\rvert E_{0_{I}}$
$\displaystyle \delta_{R}=\pi(v_{1}>v_{2})+\delta_{I}$

Backlinks

Light
Optics

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