Transmission and Reflection Coefficients of Light

This calculator computes the transmission and reflection coefficients of light at oblique incidence on a uniaxial crystal (single interface).

$n_1 \sin \theta_1 = n_0 \sin \theta_0$

$T_s = \frac{ \sin 2\theta_0 \sin 2\theta_1 }{ \sin^2(\theta_0 + \theta_1) }$

$T_p = \frac{ \sin 2\theta_0 \sin 2\theta_1 }{ \sin^2(\theta_0 + \theta_1)\cos^2(\theta_0 - \theta_1) }$

$R_p = \frac{ \tan^2(\theta_0 - \theta_1) }{ \tan^2(\theta_0 + \theta_1) }$

$R_s = \frac{ \sin^2(\theta_0 - \theta_1) }{ \sin^2(\theta_0 + \theta_1) }$

Incident angle $\theta_0$; refraction angle $\theta_1$;
s-polarized transmission coefficient $T_s$;
p-polarized transmission coefficient $T_p$;
s-polarized reflection coefficient $R_s$;
p-polarized reflection coefficient $R_p$.

Input

Incident Angle, $\theta_0$:

degree (°)

$n_0$:

$n_1$:

Output

Transmission and Reflection Coefficients of Light

$n_1 \sin \theta_1 = n_0 \sin \theta_0$

$T_s = \frac{ \sin 2\theta_0 \sin 2\theta_1 }{ \sin^2(\theta_0 + \theta_1) }$

$T_p = \frac{ \sin 2\theta_0 \sin 2\theta_1 }{ \sin^2(\theta_0 + \theta_1)\cos^2(\theta_0 - \theta_1) }$

$R_p = \frac{ \tan^2(\theta_0 - \theta_1) }{ \tan^2(\theta_0 + \theta_1) }$

$R_s = \frac{ \sin^2(\theta_0 - \theta_1) }{ \sin^2(\theta_0 + \theta_1) }$

Incident Angle, $\theta_0$:

$n_0$:

$n_1$:

$T_s$:

$T_p$:

$R_s$:

$R_p$:

Fresnel Reflection / Transmission