Angle Refraction of Light: UNIZOR.COM - Physics4Teens - Waves - Phenomena of Light
Channel: Zor Shekhtman on UNIZOR Education
Date: 2022-06-18

UNIZOR.COM - Physics through a Looking Glass of Mathematician
Notes to a video lecture on http://www.unizor.com

Angle Refraction of Light

Let's analyze what happens with a flat wave front of light, when its parallel rays fall at an angle onto a border between two transparent substances with incident rays coming from a substance with a smaller refraction index (and, therefore, higher speed of light in this substance, since refraction index is a ratio of the speed of light in the vacuum to a speed of light in the substance). For example, flat wave front of light from air falls on a glass surface.

As we know from the previous lectures, there is a dependency between refraction indices n1, n2 of (or speeds of light V1, V2 in) two bordering substances and angles θ1 of incidence and θ2 of refraction of a ray of light falling on the border:
sin(θ1)/V1 = sin(θ2)/V2
or sin(θ1)·n1 = sin(θ2)·n2
This was derived from the Fermat's Principle of the Least Time.

Now we will use the Huygens principle to analyze this process from the wave theory viewpoint and demonstrate the same result.

Situation becomes more complex, when the speed of light is not the same at different points of the wave front because the wave front falls onto a different transparent substance, for example, it falls from the air onto a glass surface.

If, for example, a flat wave front falls from the air perpendicularly to a flat glass surface, the speed of light at different points of a wave front at the same time is the same, faster for wave front in the air and slower in the glass. The light will propagate in the same direction in the glass, as it was in the air.

But, if the flat wave front falls from the air at some acute incident angle onto flat glass surface or a spherical wave front falls on a flat glass surface, those point of the wave front that reached the glass earlier will emit light at a slower speed, so the propagation of the wave front will not be the same as on the picture above.

Let's examine the behavior of the flat wave front falling from the air onto a flat glass surface at an incident angle θ1 and analyze the shape and direction of propagation of the wave front at moment in time t+Δt, knowing its position and direction at time t.