# Reflection, refraction, and Snell's law

• I
Ahmed1029
Where do the laws of reflection, refraction, and Snell's law come from in geometric optics? Are they derivable from basic laws of physics?

Gold Member
I think you can derive all these using a ruler and protractor. For Snell's Law you need first to find out the relative velocities of light in the media, using knowledge of the refractive indices.

• topsquark
2022 Award
I think you need the principle that light follows the path that minimises travel time. Then you fix two points and a flat surface, and draw a reflected/refracted ray between the points with the reflection/refraction event lying somewhere on the surface. Write down the travel time, and calculus will then find you the location of the event and you can derive the angles you want from there.

• Ahmed1029 and topsquark
Where do the laws of reflection, refraction, and Snell's law come from in geometric optics? Are they derivable from basic laws of physics?
I derive them in class as originating from conservation of (linear) momentum.

• berkeman
Staff Emeritus
Homework Helper
Where do the laws of reflection, refraction, and Snell's law come from in geometric optics? Are they derivable from basic laws of physics?
Whenever you have waves, you'll get reflection and refraction. You can derive these laws from analyzing how waves propagate through media in general. The others have indicated some approaches to doing this. Using Huygen's principle is another way.

At a little deeper level, the laws are a consequence of the boundary conditions the wave must satisfy where the two media meet. For the case of a wave propagating down a string connected to a different string, one condition arises because the strings must stay tied together, and another from the fact that the strings exert equal and opposite forces on each other, i.e., Newton's third law. For light, the electric and magnetic fields have to satisfy similar boundary conditions to satisfy Maxwell's equations.

• Ahmed1029
Ahmed1029
Whenever you have waves, you'll get reflection and refraction. You can derive these laws from analyzing how waves propagate through media in general. The others have indicated some approaches to doing this. Using Huygen's principle is another way.

At a little deeper level, the laws are a consequence of the boundary conditions the wave must satisfy where the two media meet. For the case of a wave propagating down a string connected to a different string, one condition arises because the strings must stay tied together, and another from the fact that the strings exert equal and opposite forces on each other, i.e., Newton's third law. For light, the electric and magnetic fields have to satisfy similar boundary conditions to satisfy Maxwell's equations.
So is geometric optics derived from the physics of waves? which one comes first?

Staff Emeritus
Homework Helper
Waves. Classically, light is an electromagnetic wave, after all.

Geometric optics is the limit where we can neglect the waviness of light and model light as rays, which travel in straight lines through a uniform medium.

• • malawi_glenn, Ahmed1029 and Ibix
2022 Award
That's not what I said. In that thread I said "what's wrong with the explanation on Wikipedia", to which you replied "you mean Fermat's principle", to which I replied (correctly) that Fermat's principle is not mentioned on the page about refraction (although I didn't look at the page on Snell's law, which does, so perhaps we were looking at different pages). At the time, I was not explaining, I was attempting to get you to tell us what explanations you were aware of and say what you didn't understand about them because there was no point repeating stuff you already knew.

• binis
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