Refraction through Muliple media

[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'?

 

[tiny-tim]

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'?

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?

 

[Andy Resnick]

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

 

[sr_philosophy]

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?

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.

 

[Hootenanny]

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.

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.

 

[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!

 

[Hootenanny]

Who told you i didn't know the formula?

Er...you did:

What law states that the emergent ray at then end from medium 2 to air is also 'i'?

snell's law applies only for a pair of media... if you didn't know!

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.

 

[sr_philosophy]

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

 

[Hootenanny]

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

Sorry, I misread your OP. So, you have a ray of light traveling 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.

 

[Redbelly98]

sr_philosophy, are these parallel plane surfaces?

If so, then:

n_air sin(θ_initial) = n₁ sin(θ₁)

n₁ sin(θ₁) = n₂ sin(θ₂)

n₂ sin(θ₂) = n_air sin(θ_final)

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

θ_initial = θ_final

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?