How Does Snell's Law Help Calculate Distance Between Parallel Lines?

In summary, the conversation discusses finding the proof for the distance between two parallel lines using Snell's Law and the equation sin(A+B)= sinAcosB + sinBcosA. The participants suggest using rt angled triangles and explicitly stating the desired outcome in order to prove the relation needed. It is also mentioned that some angles are related through Snell's Law and it is important to identify all relevant triangles.
  • #1
Shaun97
5
0
I can't seem to find the proof for the distance between the two parallel lines.
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Homework Equations

: Snells law: μ1sinθ1=μ2sinθ2
Sin (A+B)= sinAcosB + sinBcosA[/B]

The Attempt at a Solution

: tried using the parallel lines to get a result in terms of the initial angle of incidence ϑ, as the lateral deviation creates a right angle triangle.
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[/B]
 
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  • #2
Thats a good start... you need the other angles too.
There's another rt angled triangle that may be useful in there.
It also helps to explicitly state exactly what you want to prove.
 
  • #3
there's the rt angled triangle with alpha (α) as one of the angles and with t as the height of it, and as the answer is also in terms of t I assume it's necessary to do something with this triangle but at the same time the answer only contains one angle, ϑ.
 
  • #4
You have to start by writing down relations involving the different triangles ... then you can think about how you can use them to get the relation you need to prove.

Clearly you need to find a way to get rid of the terms that are not in the final form. Don't forget that some of the angles are related through Snell's Law. Make sure you have identified all the triangles ...
 
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Related to How Does Snell's Law Help Calculate Distance Between Parallel Lines?

1. How does light behave in geometric optics?

In geometric optics, light is treated as rays that travel in straight lines. These rays can be reflected, refracted, or absorbed by different materials, and their behavior can be described using principles such as Snell's law and the law of reflection.

2. What is the proof for the law of reflection in geometric optics?

The law of reflection states that the angle of incidence is equal to the angle of reflection. This can be proven using basic geometry and the fact that light rays travel in straight lines. When a ray of light hits a smooth, flat surface, it will bounce off at the same angle it hit the surface, creating a reflection.

3. How is Snell's law derived in geometric optics?

Snell's law describes the relationship between the angles of incidence and refraction when light passes through a boundary between two materials. It can be derived using the principle of Fermat's principle, which states that light will always follow the path that takes the shortest amount of time. Through mathematical calculations, this principle leads to the equation n₁sinθ₁ = n₂sinθ₂, where n₁ and n₂ are the refractive indices of the two materials and θ₁ and θ₂ are the angles of incidence and refraction, respectively.

4. Can the behavior of light be explained using only geometric optics?

In some cases, the behavior of light can be accurately described using only geometric optics. This is true for simple, homogeneous materials and situations where the size of the objects involved is much larger than the wavelength of the light. However, in more complex situations, such as when light interacts with microscopic structures or when it passes through multiple materials with varying refractive indices, other branches of optics, such as wave optics, must be considered.

5. How is the speed of light related to geometric optics?

In geometric optics, the speed of light is assumed to be constant and is not explicitly considered in calculations. This is because geometric optics treats light as rays that travel in straight lines, rather than waves. However, the speed of light is still an important fundamental constant that plays a role in many optical phenomena, and it is typically used to convert between different units of measurement when working with geometric optics.

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