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

[Shaun97]

I can't seem to find the proof for the distance between the two parallel lines.

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.

[/B]

 

[Simon Bridge]

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.

 

[Shaun97]

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.

 

[Simon Bridge]

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 ...