Critical Angle
While Snell's law is a simple relationship, some of the implications are important to understanding the natural world around us and also technology. You will notice that when light leaves a medium with a higher refractive index than the outside medium, that the outside angle is larger. At one point, if we progressively make the interior incident angle larger and larger, you'll find the outside angle reaches 90 degrees. What should happen if we continue to increase the interior angle?
While haven't described a theoretical basis from which to reason, the answer is that the light never leaves the higher index material, but instead reflects off the boundary. The angle beyond which such reflection takes place is called the critical angle, and the subsequent reflection is called total internal reflection. The value of the critical angle is found simply by plugging into Snell's law while using a right angle for the exterior angle. Naturally the value of the critical angle depends on the two refractive indices. When viewing the critical angle on a water/air boundary from the vantage point of the water (as in a diving scenario), one sees a circular window of the outside world through something referred to as Snell's window. A photograph of Snell's window is below.![[url=https://commons.wikimedia.org/wiki/Category:Snell%27s_window#/media/File:US_Navy_110607-N-XD935-191_Navy_Diver_2nd_Class_Ryan_Arnold,_assigned_to_Mobile_Diving_and_Salvage_Unit_2,_snorkels_on_the_surface_to_monitor_multi.jpg]"Snell's Window"[/url] by US Navy is in the [url=https://wiki.creativecommons.org/Public_domain]Public Domain[/url]
Snell's window is a simple consequence of Snell's law. The boundary of the "window" is defined by the critical angle. Beyond the critical angle the edge is dark because you see a reflection of the dark, deep waters. If this was a swimming pool with pretty Spanish tile work, you'd see a reflection of the tiles rather than darkness framing Snell's window.](https://www.geogebra.org/resource/qejaSMBS/evVAWNustAyOqynQ/material-qejaSMBS.png)