A stack of 2 parallel sheets of glass are arrayed from left to rightas shown in

Question

A stack of 2 parallel sheets of glass are arrayed from left to rightas shown in the diagram. The sheets have differing indices of refraction:n2= 1.8 andn1= 1.4. The region 0 to the right of the stack isair whose index of refraction may be taken to ben0=1.00. The region to the left of sheet 2 is of no interest.

(a) If a light beam is traveling in sheet 2 to the right at an angleofq2= 30? to thex-axis, calculate the angleq0the beam makes with respect to thex-axis when it emerges into the air on the right hand side.

q0=?

Explanation / Answer

wow, I don't think anyone is going to do this for you, this is a mostly just a large amount of small calculations,
here, go to this link ( http://hyperphysics.phy-astr.gsu.edu/hba… ) and at the bottom of the page you will find a calculating tool for finding those angles, just calculate the angle of the light emerging into layer 8 then do the same for 7 and the rest of the layers. I'd recomend sketching a big labeled drawing to keep track of the angles. Then calculate how far down the beam is traveling by using trig you can tell it equals (thickness of the layer or d)*tan(angle of the light that emerges in the layer) then sum the distances and find the difference between that sum and the distance if the beam was never refracted
the "total internal reflection" is when the angle of the beam is so step that it never penetrates and it's just reflected http://en.wikipedia.org/wiki/Total_inter… for this to happen the the angle of the beam must be within the critical angle the equation to find that is found here, http://en.wikipedia.org/wiki/Total_inter…
this problem will take a smart student at least 20 minutes to complete, for you it make take over an hour
no one is going to solve the whole thing for you, but if you asked another more simpler question to figure out how to do this then people may actually give you complete answers. you could set up a more simple situation without numbers and only 2 layers of glass and you can ask how to solve for angles, offsets and critical angles.

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