Brewster Angle Calculator
Brewster Angle Calculator computes the Brewster angle and reflection coefficients at a dielectric interface.
Formulas Used in Brewster Angle Calculator
The calculator computes the Brewster angle and reflection coefficients for light at an interface between two media:
Brewster Angle:
\\[ \theta_B = \arctan\left(\frac{n_2}{n_1}\right) \\]Fresnel Reflection Coefficients:
\\[ r_s = \frac{n_1 \cos \theta_i – n_2 \cos \theta_t}{n_1 \cos \theta_i + n_2 \cos \theta_t}, \quad r_p = \frac{n_2 \cos \theta_i – n_1 \cos \theta_t}{n_2 \cos \theta_i + n_1 \cos \theta_t} \\]Snell’s Law:
\\[ n_1 \sin \theta_i = n_2 \sin \theta_t \\]Where:
- \\( \theta_B \\): Brewster angle (degrees)
- \\( n_1 \\): Refractive index of incident medium
- \\( n_2 \\): Refractive index of refracted medium
- \\( \theta_i \\): Angle of incidence (degrees)
- \\( \theta_t \\): Angle of transmission (degrees)
- \\( r_s \\), \\( r_p \\): Reflection coefficients for s- and p-polarized light
At \\( \theta_i = \theta_B \\), \\( r_p = 0 \\).
Example Calculations
Example 1: Air (n₁ = 1.0) to Glass (n₂ = 1.5)
Input: \\( n_1 = 1.0, n_2 = 1.5 \\)
\\[
\theta_B = \arctan\left(\frac{1.5}{1.0}\right) \approx 56.31^\circ
\\]
Result: \\( \theta_B \approx 56.31^\circ \\)
Example 2: Glass (n₁ = 1.5) to Air (n₂ = 1.0)
Input: \\( n_1 = 1.5, n_2 = 1.0 \\)
\\[
\theta_B = \arctan\left(\frac{1.0}{1.5}\right) \approx 33.69^\circ
\\]
Result: \\( \theta_B \approx 33.69^\circ \\)