Snells Law and refractive index

[jsmith613]

Snells law states that refractive index = (speed in medium 1)/(speed in medium 2)
alternativley
1 μ2 = sin i / sin r

Why therefore does Snells law also equal:

μ1 * sin(angle-1) = μ2 * sin(angle-2)

and for a critical angle


μ1 sin C = μ2 sin 90

thanks

 

[jsmith613]

Can I split 1 μ2 into μ1/μ2

 

[Redbelly98]

Snells law states that refractive index = (speed in medium 1)/(speed in medium 2)

Not quite. Actually,

Refractive index of medium = n (or μ) = (speed in vacuum) / (speed in medium)​

Plus, this isn't Snell's Law , it's the definition of the refractive index.

. . . alternativley
1 μ2 = sin i / sin r

Okay, it looks like you are using μ instead of n for refractive index. Well, the above equation is only true if medium 1 has μ1=1. It's not true in general.

Why therefore does Snells law also equal:

μ1 * sin(angle-1) = μ2 * sin(angle-2)

That is the equation for Snell's Law . Make the following substitutions, and you can get your previous equation:

μ1=1
angle-1 = i
angle-2 = r​

. . . and for a critical angleμ1 sin C = μ2 sin 90

thanks

The critical angle (of incidence) occurs when the refracted angle is 90°. Larger angles of incidence would require sin(r)>1 to satisfy Snell's Law, which is impossible.

By the way, the basics of Snell's Law are given here:

https://www.physicsforums.com/library.php?do=view_item&itemid=226

 

[jsmith613]

ok then, so why is Snell's Law as it is. What is the mathmatical proof?

thanks

 

[jtbell]

There are several ways to derive Snell's Law, depending on what you take as your starting point (assumptions). This is the one you find in most introductory textbooks:

http://www.vias.org/physics/bk5_04_02_06.html

The Wikipedia article on Snell's law describes a few others:

http://en.wikipedia.org/wiki/Snell's_law

(I found these with a Google search for "Snell's Law derivation", by the way.)