Editing Fresnel equations (section)

=== Non-magnetic media ===
Since the Fresnel equations were developed for optics, they are usually given for non-magnetic materials. Dividing ({{EquationNote|4}}) by ({{EquationNote|5}})) yields
<math display=block>Y=\frac{n}{\,c\mu\,}\,.</math>
For non-magnetic media we can substitute the [[vacuum permeability]] {{math|''μ''<sub>0</sub>}} for {{math|''μ''}}, so that
<math display=block>Y_1=\frac{n_1}{\,c\mu_0} ~~;~~~ Y_2=\frac{n_2}{\,c\mu_0}\,;</math>
that is, the admittances are simply proportional to the corresponding refractive indices. When we make these substitutions in equations ({{EquationNote|13}}) to ({{EquationNote|16}}) and equations ({{EquationNote|21}}) to ({{EquationNote|26}}), the factor ''cμ''<sub>0</sub> cancels out. For the amplitude coefficients we obtain:<ref name=Sernelius /><ref name="Born 1970" />

{{NumBlk|:|<math>r_\text{s}=\frac{n_1\cos\theta_\text{i}-n_2\cos\theta_\text{t}}{n_1\cos\theta_\text{i}+n_2\cos\theta_\text{t}}</math>|{{EquationRef|29}}}}
{{NumBlk|:|<math>t_\text{s}=\frac{2n_1\cos\theta_\text{i}}{n_1\cos\theta_\text{i}+n_2\cos\theta_\text{t}}\,</math>|{{EquationRef|30}}}}

{{NumBlk|:|<math>r_\text{p}=\frac{n_2\cos\theta_\text{i}-n_1\cos\theta_\text{t}}{n_2\cos\theta_\text{i}+n_1\cos\theta_\text{t}}</math>|{{EquationRef|31}}}}<!-- PLEASE DON'T CHANGE THE SIGN OF THIS EXPRESSION JUST BECAUSE YOUR FAVORITE TEXTBOOK USES A DIFFERENT SIGN CONVENTION FROM THE ONE DEFINED IN THIS ARTICLE AND ITS REFERENCES. -->
{{NumBlk|:|<math>t_\text{p}=\frac{2n_1\cos\theta_\text{i}}{n_2\cos\theta_\text{i}+n_1\cos\theta_\text{t}}\,.</math>|{{EquationRef|32}}}}

For the case of normal incidence these reduce to:

{{NumBlk|:|<math>r_\text{s0}=\frac{n_1-n_2}{n_1+n_2}</math>|{{EquationRef|33}}}}
{{NumBlk|:|<math>t_\text{s0}=\frac{2n_1}{n_1+n_2}</math>|{{EquationRef|34}}}}

{{NumBlk|:|<math>r_\text{p0}=\frac{n_2-n_1}{n_2+n_1}</math>|{{EquationRef|35}}}}
{{NumBlk|:|<math>t_\text{p0}=\frac{2n_1}{n_2+n_1}\,.</math>|{{EquationRef|36}}}}

The power reflection coefficients become:
{{NumBlk|:|<math>R_\text{s}=\left|\frac{n_1\cos\theta_\text{i}-n_2\cos\theta_\text{t}}{n_1\cos\theta_\text{i}+n_2\cos\theta_\text{t}}\right|^2</math>|{{EquationRef|37}}}}
{{NumBlk|:|<math>R_\text{p}=\left|\frac{n_2\cos\theta_\text{i}-n_1\cos\theta_\text{t}}{n_2\cos\theta_\text{i}+n_1\cos\theta_\text{t}}\right|^2\,.</math>|{{EquationRef|38}}}}
The power transmissions can then be found from {{math|''T''{{nnbsp}}{{=}}{{nnbsp}}1{{nnbsp}}−{{nnbsp}}''R''}}.