A stack of 2 parallel sheets of glass are arrayed from left to right as shown in
ID: 1327307 • Letter: A
Question
A stack of 2 parallel sheets of glass are arrayed from left to right as shown in the diagram. The sheets have differing indices of refraction: n2 = 1.8 and n1 = 1.4. The region 0 to the right of the stack is air whose index of refraction may be taken to be n0 = 1.00. The region to the left of sheet 2 is of no interest.
1)If a light beam is traveling in sheet 2 to the right at an angle of 2 = 30° to the x-axis, calculate the angle 0 the beam makes with respect to the x-axis when it emerges into the air on the right hand side.
0 =
°
2)If you want the beam to undergo total internal reflection at the first interface (the interface between sheet 2 and sheet 1), what is the minimum angle the incoming beam (the beam traveling in the sheet 2) must make with the x-axis?
2 =
°
3)If you want the beam to undergo total internal reflection at the second interface (the interface between sheet 1 and the air), what is the minimum angle the incoming beam (the beam traveling in the sheet 2) must make with the x-axis?
2 =
°
4)If a light beam is traveling in sheet 2 to the right at an angle of 2 = 45° to the x-axis, the beam eventually returns to sheet 2 (after undergoing total internal reflection at one of the interfaces). At what angle 2' with respect to the x-axis does the return beam travel in sheet 2?
2 =
Explanation / Answer
Use snell's law to calculate the incident angle
no sin 0 = n2 sin theta
1 sin 0= 1.8 sin 30
0 = sin^-1 ( 1.8 sin 30) = 64.15 degree
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Apply law between n1 and n2 medium
1.8*sin(2)=1.4*sin90
2=51.06
-----------------------------------------
Apply law to no and n1 medium
1.8*sin(2)=1*sin90
2 = sin^-1 ( 1/1.8) =33.749
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2=45
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