Editing Fresnel equations (section)

=== Special cases ===
==== Normal incidence ====
For the case of [[normal incidence]], {{math|1=''θ''{{sub|i}} = ''θ''{{sub|t}} = 0}}, and there is no distinction between s and p polarization.  Thus, the reflectance simplifies to
<math display=block>
R_0 = \left|\frac{n_1  - n_2 }{n_1 + n_2 }\right|^2\,.
</math>

For common glass ({{math|''n''<sub>2</sub> ≈ 1.5}}) surrounded by air ({{math|1=''n''<sub>1</sub> = 1}}), the power reflectance at normal incidence can be seen to be about 4%, or 8% accounting for both sides of a glass pane.

==== Brewster's angle ====
{{Main|Brewster's angle}}
At a dielectric interface from  {{math|''n''<sub>1</sub>}} to {{math|''n''<sub>2</sub>}}, there is a particular angle of incidence at which {{math|''R''<sub>p</sub>}} goes to zero and a p-polarised incident wave is purely refracted, thus all reflected light is s-polarised. This angle is known as [[Brewster's angle]], and is around 56° for {{math|1=''n''<sub>1</sub> = 1}} and {{math|1=''n''<sub>2</sub> = 1.5}} (typical glass).

==== Total internal reflection ====
{{Main|Total internal reflection}}
When light travelling in a denser medium strikes the surface of a less dense medium (i.e., {{math|1=''n''<sub>1</sub> &gt; ''n''<sub>2</sub>}}), beyond a particular incidence angle known as the ''critical angle'', all light is reflected and {{math|1=''R''<sub>s</sub> = ''R''<sub>p</sub> = 1}}. This phenomenon, known as [[total internal reflection]], occurs at incidence angles for which Snell's law predicts that the sine of the angle of refraction would exceed unity (whereas in fact {{math|sin{{nnbsp}}''θ'' ≤ 1}} for all real {{math|''θ''}}). For glass with {{math|1=''n'' = 1.5}} surrounded by air, the critical angle is approximately 42°.

==== 45° incidence ====
Reflection at 45° incidence is very commonly used for making 90° turns. For the case of light traversing from a less dense medium into a denser one at 45° incidence ({{math|1=''θ'' = 45°}}), it follows algebraically from the above equations that {{math|''R''<sub>p</sub>}} equals the square of {{math|''R''<sub>s</sub>}}:
<math display=block> R_\text{p} = R_\text{s}^2 </math>

This can be used to either verify the consistency of the measurements of {{math|''R''<sub>s</sub>}} and {{math|''R''<sub>p</sub>}}, or to derive one of them when the other is known. This relationship is only valid for the simple case of a single plane interface between two homogeneous materials, not for films on substrates, where a more complex analysis is required.

Measurements of {{math|''R''<sub>s</sub>}} and {{math|''R''<sub>p</sub>}} at 45° can be used to estimate the reflectivity at normal incidence.{{cn|date=October 2023}} The "average of averages" obtained by calculating first the arithmetic as well as the geometric average of {{math|''R''<sub>s</sub>}} and {{math|''R''<sub>p</sub>}}, and then averaging these two averages again arithmetically, gives a value for {{math|''R''<sub>0</sub>}} with an error of less than about 3% for most common optical materials.{{cn|date=October 2023|reason=source needed to establish accuracy.}} This is useful because measurements at normal incidence can be difficult to achieve in an experimental setup since the incoming beam and the detector will obstruct each other. However, since the dependence of {{math|''R''<sub>s</sub>}} and {{math|''R''<sub>p</sub>}} on the angle of incidence for angles below 10° is very small, a measurement at about 5° will usually be a good approximation for normal incidence, while allowing for a separation of the incoming and reflected beam.