Refraction through Muliple media

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In summary, a ray of light traveling through air and entering and exiting two different media will undergo refraction at each interface. The initial incident angle between air and the first medium is equal to the emergent angle between the second medium and air. This follows Snell's law and the geometry theorem of alternate-interior angles for parallel lines cut by a transversal.
  • #1
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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  • #2
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:
 
  • #3
That's only true for planar interfaces- otherwise, lenses would have no optical power.
 
  • #4
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.
 
  • #5
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.
 
  • #6
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
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.
 
  • #8
no! i wish i had a figure to explain things better!
 
  • #9
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?
 

FAQ: Refraction through Muliple media

What is refraction through multiple media?

Refraction through multiple media is the phenomenon of light bending as it passes through different materials or substances with varying optical properties. This can include passing through air, water, glass, or other transparent materials.

How does refraction through multiple media occur?

Refraction occurs due to a change in the speed of light as it moves from one medium to another. This change in speed causes the light to bend, and the amount of bending is dependent on the difference in refractive indices between the two media.

What is the law of refraction?

The law of refraction, also known as Snell's law, states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equivalent to the ratio of the velocities of light in the two media. This can be represented by the equation: n1 sinθ1 = n2 sinθ2, where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively.

How does the refractive index affect refraction through multiple media?

The refractive index is a measure of how much a material can slow down the speed of light. A higher refractive index means that light is slowed down more, resulting in a larger change in direction when passing through a different medium. This is why light bends more when passing through materials with higher refractive indices.

What are some real-world applications of refraction through multiple media?

Refraction through multiple media has many practical applications, including the creation of lenses for glasses and cameras, the phenomenon of mirages, and the way light is dispersed in a prism. It is also important in understanding how light travels through the Earth's atmosphere and how it affects the visibility of celestial objects.

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