(d) If a light beam is traveling in sheet 2 to the right at an angleof q 2 = 45?
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Question
(d) If a light beam is traveling in sheet 2 to the right at an angleofq2= 45? to thex-axis, the beameventually returns to sheet 2 (after undergoing total internal reflection at one of the interfaces). At whatangleq2' with respect to the x-axis doesthe return beam travel in sheet 2?
q2' =?
(d) If a light beam is traveling in sheet 2 to the right at an angleofq2= 45? to thex-axis, the beameventually returns to sheet 2 (after undergoing total internal reflection at one of the interfaces). At whatangleq2' with respect to the x-axis doesthe return beam travel in sheet 2? q2' =Explanation / Answer
A stack of 9 parallel sheets of glass are arrayed from left to right as shown in the diagram. The sheets have a common, uniform thickness d = 2 cm, but differing indices of refraction: n9 = 1.9, n8 = 1.80, ..., n1 = 1.10. 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 9 is of no interest.
(a) If a light beam is traveling in sheet 9 to the right at an angle of 9 = 30° to the x-axis, calculate the angle q0 the beam makes with respect to the x-axis when it emerges into the air on the right hand side. Enter the angle as a number of degrees (with no degree symbol or units).
0 = ? °
(b) Calculate the magnitude of the total offset in the y-direction of the emerging beam measured from the beams position at interface between the sheets 9 and 8 and its position at the position of emergence into the air at the interface with sheet 1.
y = ? cm
(c) If the angle of incidence of the beam in sheet 9 is changed to 9 = 55°, at what interface in the stack does the beam undergo total internal reflection.
Specify the interface in decimal notation according to the following scheme: if the reflection occurs at the sheet 9-sheet 8 interface, answer 8.5; if at the sheet 8-sheet 7 interface, answer 7.5, etc.
interface = ?
(d) Under the conditions of part (c), the beam eventually returns to sheet 9. At what angle 9' with respect to the x-axis does the return beam travel in sheet 9?
9' = ? °
(e) Under the conditions of part (c), calculate the magnitude of the total offset y' in the y-direction of the beam as measured between the points of entrance and exit at the sheet 9-sheet 8 interface.
y' = ? cm
A stack of 9 parallel sheets of glass are arrayed from left to right as shown in the diagram. The sheets have a common, uniform thickness d = 2 cm, but differing indices of refraction: n9 = 1.9, n8 = 1.80, ..., n1 = 1.10. 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 9 is of no interest.
(a) If a light beam is traveling in sheet 9 to the right at an angle of 9 = 30° to the x-axis, calculate the angle q0 the beam makes with respect to the x-axis when it emerges into the air on the right hand side. Enter the angle as a number of degrees (with no degree symbol or units).
0 = ? °
(b) Calculate the magnitude of the total offset in the y-direction of the emerging beam measured from the beams position at interface between the sheets 9 and 8 and its position at the position of emergence into the air at the interface with sheet 1.
y = ? cm
(c) If the angle of incidence of the beam in sheet 9 is changed to 9 = 55°, at what interface in the stack does the beam undergo total internal reflection.
Specify the interface in decimal notation according to the following scheme: if the reflection occurs at the sheet 9-sheet 8 interface, answer 8.5; if at the sheet 8-sheet 7 interface, answer 7.5, etc.
interface = ?
(d) Under the conditions of part (c), the beam eventually returns to sheet 9. At what angle 9' with respect to the x-axis does the return beam travel in sheet 9?
9' = ? °
(e) Under the conditions of part (c), calculate the magnitude of the total offset y' in the y-direction of the beam as measured between the points of entrance and exit at the sheet 9-sheet 8 interface.
y' = ? cm
A stack of 9 parallel sheets of glass are arrayed from left to right as shown in the diagram. The sheets have a common, uniform thickness d = 2 cm, but differing indices of refraction: n9 = 1.9, n8 = 1.80, ..., n1 = 1.10. 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 9 is of no interest.
(a) If a light beam is traveling in sheet 9 to the right at an angle of 9 = 30° to the x-axis, calculate the angle q0 the beam makes with respect to the x-axis when it emerges into the air on the right hand side. Enter the angle as a number of degrees (with no degree symbol or units).
0 = ? °
(b) Calculate the magnitude of the total offset in the y-direction of the emerging beam measured from the beams position at interface between the sheets 9 and 8 and its position at the position of emergence into the air at the interface with sheet 1.
y = ? cm
(c) If the angle of incidence of the beam in sheet 9 is changed to 9 = 55°, at what interface in the stack does the beam undergo total internal reflection.
Specify the interface in decimal notation according to the following scheme: if the reflection occurs at the sheet 9-sheet 8 interface, answer 8.5; if at the sheet 8-sheet 7 interface, answer 7.5, etc.
interface = ?
(d) Under the conditions of part (c), the beam eventually returns to sheet 9. At what angle 9' with respect to the x-axis does the return beam travel in sheet 9?
9' = ? °
(e) Under the conditions of part (c), calculate the magnitude of the total offset y' in the y-direction of the beam as measured between the points of entrance and exit at the sheet 9-sheet 8 interface.
y' = ? cm 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 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 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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