Mixing
Validify this property of an ellipse. [closed]
Imagine a 2D ellipse with a little hole in it. We pass a light ray from that hole to one of the focus. The interior of the ellipse is reflective and so light ray will pass through other focus due to its property. Interestingly asymptotically, the light ray will converge on the major axis means light ray will toggle between two points of the major axis.Please follow this link
conic-sections
edited Nov 21 '18 at 9:25
Vee Hua Zhi
759224
asked Nov 21 '18 at 9:11
YashM
61
closed as unclear what you're asking by Delta-u, John B, Davide Giraudo, Don Thousand, Aretino Nov 21 '18 at 21:58
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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Imagine a 2D ellipse with a little hole in it. We pass a light ray from that hole to one of the focus. The interior of the ellipse is reflective and so light ray will pass through other focus due to its property. Interestingly asymptotically, the light ray will converge on the major axis means light ray will toggle between two points of the major axis.Please follow this link
conic-sections
edited Nov 21 '18 at 9:25
Vee Hua Zhi
759224
asked Nov 21 '18 at 9:11
YashM
61
closed as unclear what you're asking by Delta-u, John B, Davide Giraudo, Don Thousand, Aretino Nov 21 '18 at 21:58
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
This is theorem 2.8 on page 10 here: math.uchicago.edu/~may/REU2014/REUPapers/Park.pdf
– Aretino
Nov 21 '18 at 22:00
add a comment |
Imagine a 2D ellipse with a little hole in it. We pass a light ray from that hole to one of the focus. The interior of the ellipse is reflective and so light ray will pass through other focus due to its property. Interestingly asymptotically, the light ray will converge on the major axis means light ray will toggle between two points of the major axis.Please follow this link
conic-sections
edited Nov 21 '18 at 9:25
Vee Hua Zhi
759224
asked Nov 21 '18 at 9:11
YashM
61
Imagine a 2D ellipse with a little hole in it. We pass a light ray from that hole to one of the focus. The interior of the ellipse is reflective and so light ray will pass through other focus due to its property. Interestingly asymptotically, the light ray will converge on the major axis means light ray will toggle between two points of the major axis.Please follow this link
conic-sections
conic-sections
edited Nov 21 '18 at 9:25
Vee Hua Zhi
759224
asked Nov 21 '18 at 9:11
YashM
61
edited Nov 21 '18 at 9:25
Vee Hua Zhi
759224
asked Nov 21 '18 at 9:11
YashM
61
edited Nov 21 '18 at 9:25
Vee Hua Zhi
759224
edited Nov 21 '18 at 9:25
Vee Hua Zhi
759224
edited Nov 21 '18 at 9:25
Vee Hua Zhi
759224
759224
asked Nov 21 '18 at 9:11
YashM
61
asked Nov 21 '18 at 9:11
YashM
61
asked Nov 21 '18 at 9:11
YashM
61
61
closed as unclear what you're asking by Delta-u, John B, Davide Giraudo, Don Thousand, Aretino Nov 21 '18 at 21:58
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Delta-u, John B, Davide Giraudo, Don Thousand, Aretino Nov 21 '18 at 21:58
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
This is theorem 2.8 on page 10 here: math.uchicago.edu/~may/REU2014/REUPapers/Park.pdf
– Aretino
Nov 21 '18 at 22:00
add a comment |
This is theorem 2.8 on page 10 here: math.uchicago.edu/~may/REU2014/REUPapers/Park.pdf
– Aretino
Nov 21 '18 at 22:00
This is theorem 2.8 on page 10 here: math.uchicago.edu/~may/REU2014/REUPapers/Park.pdf
– Aretino
Nov 21 '18 at 22:00
This is theorem 2.8 on page 10 here: math.uchicago.edu/~may/REU2014/REUPapers/Park.pdf
– Aretino
Nov 21 '18 at 22:00
add a comment |
1 Answer
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First consider the case where the light beam exits one focus in a direction that is initially away from the other focus. Then this property holds, since the angle to the major axis must decrease.
From there, we can also solve the case where, after leaving one focus, the light beam hits the ellipse between the foci. This means that it will hit the second focus in such a way that it leaves away from the first focus, and we are back to case one.
Then, we consider the case where the light beam leaves the focus and hits the ellipse behind the second focus. In this case, the exact opposite reasoning of case one applies, and the angle to the major axis must increase. Of course this cannot happen indefinitely, and so one of the other two cases must eventually apply.
That only leaves the case where the beam hits directly perpendicular to the other focus. This can be manually checked.
answered Nov 21 '18 at 9:32
DreamConspiracy
9001216
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
First consider the case where the light beam exits one focus in a direction that is initially away from the other focus. Then this property holds, since the angle to the major axis must decrease.
From there, we can also solve the case where, after leaving one focus, the light beam hits the ellipse between the foci. This means that it will hit the second focus in such a way that it leaves away from the first focus, and we are back to case one.
Then, we consider the case where the light beam leaves the focus and hits the ellipse behind the second focus. In this case, the exact opposite reasoning of case one applies, and the angle to the major axis must increase. Of course this cannot happen indefinitely, and so one of the other two cases must eventually apply.
That only leaves the case where the beam hits directly perpendicular to the other focus. This can be manually checked.
answered Nov 21 '18 at 9:32
DreamConspiracy
9001216
add a comment |
First consider the case where the light beam exits one focus in a direction that is initially away from the other focus. Then this property holds, since the angle to the major axis must decrease.
From there, we can also solve the case where, after leaving one focus, the light beam hits the ellipse between the foci. This means that it will hit the second focus in such a way that it leaves away from the first focus, and we are back to case one.
Then, we consider the case where the light beam leaves the focus and hits the ellipse behind the second focus. In this case, the exact opposite reasoning of case one applies, and the angle to the major axis must increase. Of course this cannot happen indefinitely, and so one of the other two cases must eventually apply.
That only leaves the case where the beam hits directly perpendicular to the other focus. This can be manually checked.
answered Nov 21 '18 at 9:32
DreamConspiracy
9001216
add a comment |
First consider the case where the light beam exits one focus in a direction that is initially away from the other focus. Then this property holds, since the angle to the major axis must decrease.
From there, we can also solve the case where, after leaving one focus, the light beam hits the ellipse between the foci. This means that it will hit the second focus in such a way that it leaves away from the first focus, and we are back to case one.
Then, we consider the case where the light beam leaves the focus and hits the ellipse behind the second focus. In this case, the exact opposite reasoning of case one applies, and the angle to the major axis must increase. Of course this cannot happen indefinitely, and so one of the other two cases must eventually apply.
That only leaves the case where the beam hits directly perpendicular to the other focus. This can be manually checked.
answered Nov 21 '18 at 9:32
DreamConspiracy
9001216
First consider the case where the light beam exits one focus in a direction that is initially away from the other focus. Then this property holds, since the angle to the major axis must decrease.
From there, we can also solve the case where, after leaving one focus, the light beam hits the ellipse between the foci. This means that it will hit the second focus in such a way that it leaves away from the first focus, and we are back to case one.
Then, we consider the case where the light beam leaves the focus and hits the ellipse behind the second focus. In this case, the exact opposite reasoning of case one applies, and the angle to the major axis must increase. Of course this cannot happen indefinitely, and so one of the other two cases must eventually apply.
That only leaves the case where the beam hits directly perpendicular to the other focus. This can be manually checked.
answered Nov 21 '18 at 9:32
DreamConspiracy
9001216
answered Nov 21 '18 at 9:32
DreamConspiracy
9001216
answered Nov 21 '18 at 9:32
DreamConspiracy
9001216
answered Nov 21 '18 at 9:32
DreamConspiracy
9001216
9001216
add a comment |
add a comment |
This is theorem 2.8 on page 10 here: math.uchicago.edu/~may/REU2014/REUPapers/Park.pdf
– Aretino
Nov 21 '18 at 22:00