Refraction through Muliple media

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Discussion Overview

The discussion revolves around the behavior of light rays as they refract through multiple media, specifically focusing on the angles of incidence and emergence when transitioning between air and two different media. Participants explore the applicability of Snell's law in this context and the conditions under which it holds true.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions what law states that the emergent ray from medium 2 back to air has the same angle 'i' as the incident angle at the first interface.
  • Another participant suggests that the refractive index between the two media should be considered for a complete understanding of the situation.
  • Some participants argue that the equality of angles is only valid for planar interfaces, implying that lenses would behave differently.
  • A participant asserts that Snell's law applies only to pairs of media, challenging the assumption that it can be applied directly in this multi-media scenario.
  • Another participant clarifies that Snell's law can be applied sequentially at each interface, suggesting that it can still yield the same initial and final angles under certain conditions.
  • There is a request for a visual aid to better explain the concepts being discussed.
  • One participant provides a mathematical formulation using Snell's law at each interface, leading to the conclusion that the initial and final angles are equal under specific conditions.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of Snell's law in this scenario, with some asserting it can be applied multiple times while others argue it is limited to pairs of media. The discussion remains unresolved regarding the conditions under which the emergent angle equals the incident angle.

Contextual Notes

There are limitations regarding the assumptions about the geometry of the media interfaces, as well as the potential need for visual representations to clarify the discussion. The application of Snell's law in multi-media scenarios is also under scrutiny.

sr_philosophy
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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'?
 
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sr_philosophy said:
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! :wink:

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? :smile:
 
That's only true for planar interfaces- otherwise, lenses would have no optical power.
 
tiny-tim said:
Hi sr_philosophy! :wink:

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? :smile:

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.
 
sr_philosophy said:
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.
 
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!
 
sr_philosophy said:
Who told you i didn't know the formula?
Er...you did:
sr_philosophy said:
What law states that the emergent ray at then end from medium 2 to air is also 'i'?
sr_philosophy said:
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.
 
no! i wish i had a figure to explain things better!
 
sr_philosophy said:
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.
 
  • #10
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?
 

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