# Refraction through Muliple media

1. Nov 21, 2008

### sr_philosophy

Consider a ray of light in air traveling towards a medium 1 and then subsequently to a medium 2 and then back to air again undergoes refraction at every pair of media. Let us say that the initial incident angle between air and medium 1 is 'i'. What law states that the emergent ray at then end from medium 2 to air is also 'i'?

2. Nov 21, 2008

### tiny-tim

Hi sr_philosophy!

Hint: if the refractive index between air and medium 1 is n1, and between air and medium 2 is n2, what is the refractive index between medium 1 and medium 2?

3. Nov 21, 2008

### Andy Resnick

That's only true for planar interfaces- otherwise, lenses would have no optical power.

4. Nov 22, 2008

### sr_philosophy

no no! if u look back at the history, the formula was derived after they knew that the angles were equal. That is not a hint. Sorry.

5. Nov 22, 2008

### Hootenanny

Staff Emeritus
Really? How do you know that if you don't know what the formula is? Could you provide a reference?

In any case, the result you require (as well as the more general Snell's law which tim referenced) follows quite trivially from applying the appropriate boundary conditions to Maxwell's equations.

6. Nov 22, 2008

### sr_philosophy

Who told you i didn't know the formula? its not enough if you just know the formula... snell's law applies only for a pair of media... if you didn't know!

7. Nov 22, 2008

### Hootenanny

Staff Emeritus
Er...you did:
Indeed it does, but as tiny-tim said, you can apply Snell's law here by first applying it when the ray enters medium 2 from medium 1 and then applying it again as the ray leaves medium 2 and enters medium 1.

8. Nov 22, 2008

### sr_philosophy

no! i wish i had a figure to explain things better!

9. Nov 22, 2008

### Hootenanny

Staff Emeritus
Sorry, I misread your OP. So, you have a ray of light travelling through air, which then enters medium 1, subsequently entering medium 2 and then exiting medium 2 back into the air, yes?

If this is the case, then Snell's law is still applicable, you simply have to apply it three times, once at each interface.

10. Nov 23, 2008

### Redbelly98

Staff Emeritus
sr_philosophy, are these parallel plane surfaces?

If so, then:

nair sin(θinitial) = n1 sin(θ1)

n1 sin(θ1) = n2 sin(θ2)

n2 sin(θ2) = nair sin(θfinal)

These 3 Snell's Law equations can be combined to show that

θinitial = θfinal

So the answer is Snell's law, plus the geometry theorem (or postulate?) that alternate-interior angles are congruent for a pair of parallel lines cut by a transversal.

Or did I misunderstand what you're describing?