The Lazy Laser Physicist
You have a setup like in the image above. But it seems like detector A does some weird things. You should better check it with detector B. What is the minimum number of mirrors you have to move (translate and rotate arbitrarily) to bring the laser beam onto detector B?
- Please leave the mirrors which are used to direct the laser to detector A as they are, because if it turns out detector A is not broken you want to switch back to it. I mean it's quite well shielded from stray light compared to detector B.
- The thick black lines are walls. Please don't burn any holes in them.
- The mirrors all look the same. They have only one side (blue) with reflective coating.
- The grey grid is only for orientation.
- The detectors work for any angle of incidence.
- Make sure that the beam actually hits the detector, not only stray light.
- And don't look into the laser beam.
visual geometry physics
asked 2 hours ago
A. P.
3,20011041
add a comment |
You have a setup like in the image above. But it seems like detector A does some weird things. You should better check it with detector B. What is the minimum number of mirrors you have to move (translate and rotate arbitrarily) to bring the laser beam onto detector B?
- Please leave the mirrors which are used to direct the laser to detector A as they are, because if it turns out detector A is not broken you want to switch back to it. I mean it's quite well shielded from stray light compared to detector B.
- The thick black lines are walls. Please don't burn any holes in them.
- The mirrors all look the same. They have only one side (blue) with reflective coating.
- The grey grid is only for orientation.
- The detectors work for any angle of incidence.
- Make sure that the beam actually hits the detector, not only stray light.
- And don't look into the laser beam.
visual geometry physics
asked 2 hours ago
A. P.
3,20011041
add a comment |
You have a setup like in the image above. But it seems like detector A does some weird things. You should better check it with detector B. What is the minimum number of mirrors you have to move (translate and rotate arbitrarily) to bring the laser beam onto detector B?
- Please leave the mirrors which are used to direct the laser to detector A as they are, because if it turns out detector A is not broken you want to switch back to it. I mean it's quite well shielded from stray light compared to detector B.
- The thick black lines are walls. Please don't burn any holes in them.
- The mirrors all look the same. They have only one side (blue) with reflective coating.
- The grey grid is only for orientation.
- The detectors work for any angle of incidence.
- Make sure that the beam actually hits the detector, not only stray light.
- And don't look into the laser beam.
visual geometry physics
asked 2 hours ago
A. P.
3,20011041
You have a setup like in the image above. But it seems like detector A does some weird things. You should better check it with detector B. What is the minimum number of mirrors you have to move (translate and rotate arbitrarily) to bring the laser beam onto detector B?
- Please leave the mirrors which are used to direct the laser to detector A as they are, because if it turns out detector A is not broken you want to switch back to it. I mean it's quite well shielded from stray light compared to detector B.
- The thick black lines are walls. Please don't burn any holes in them.
- The mirrors all look the same. They have only one side (blue) with reflective coating.
- The grey grid is only for orientation.
- The detectors work for any angle of incidence.
- Make sure that the beam actually hits the detector, not only stray light.
- And don't look into the laser beam.
visual geometry physics
visual geometry physics
asked 2 hours ago
A. P.
3,20011041
asked 2 hours ago
A. P.
3,20011041
edited 2 hours ago
asked 2 hours ago
A. P.
3,20011041
asked 2 hours ago
A. P.
3,20011041
asked 2 hours ago
A. P.
3,20011041
3,20011041
add a comment |
add a comment |
4 Answers
4
active
oldest
votes
With some minor fidgeting, I'm pretty confident a setup like this can work well. Just move any unused mirror into the blue spot as shown:
answered 2 hours ago
greenturtle3141
5,22311952
Creative idea, but unfortunately mirrors are not that creative. Keeping the reflected angle the same as the incident angle, the beam has the same direction after being reflected from two parallel or orthogonal mirrors. So the downwards tendency after the inserted mirror should be the same two mirrors later.
– A. P.
2 hours ago
add a comment |
I found a solution with 2 mirrors:
answered 1 hour ago
Display name
840216
add a comment |
Assuming only 45 degree mirrors,
We are going to need two moves, and there are several ways to do it.
But since the detectors are omnidirectional, we can do better:
First take a look at the two mirrors nearest detector B. Mark the position of B' as the location of the detector B as seen through the nearest mirror. Then mark position B'', which is B', as seen through the second mirror. From that point, draw a straight line to the center of the third mirror in the very rightmost column.
Notice that the line moves 1 square sideways in 6 vertical squares. It also passes through a mirror in between. Pick up this mirror, we'll use it when we figure out where to place it.
Now, continue the line 6 squares to the left, during which time it moves 1 square up, because of the reflected angle. What joy, we are at a spot through which the original beam passes, so we can move the mirror we picked up here. We must place the mirror at an angle that is half of the beams angle ($text{arctan}(1/6) approx 9.5°$), or about 4.7 degrees, in order to hit the detector.
Like so:
answered 28 mins ago
Bass
27.1k465168
Nice explanation! rot13(Gurer vf ng yrnfg bar zber fvzvyne fbyhgvba, gurersber V jvyy jnvg fbzr gvzr orsber V npprcg gur nafjre jvgu gur uvturfg fpber.)
– A. P.
15 mins ago
add a comment |
Possibly you could
do it with one mirror
if you
can position the mirror pointed to by the blue arrow as show below in blue in front of the mirror used by detector A and reflect directly to the detector (Thanks Dr Xorile)
Shown here
answered 2 hours ago
SteveV
5,3652629
But here you changed one of the mirrors that are used to direct the beam onto detector A.
– A. P.
2 hours ago
sorry @A.P. .i'll clear up what i meant.... rot13(chg n qvssrerag zveebe va sebag bs gur bar hfrq sbe qrgrpgbe N)
– SteveV
2 hours ago
Ok that would solve the aforementioned problem. But what I don't like about this solution is that you only direct stray light into detector B, not the whole beam. I will make this point clear in the question.
– A. P.
2 hours ago
@A.P. I'm not sure what you mean. Why would it be stray light? if they are perfect mirrors, you will get the whole beam. What i'm not sure about is if there is a gap big enough to hit the second mirror by detector B at the right angle, but thats what I'm trying! i suggest using a low power laser to check :)
– SteveV
2 hours ago
The "oblique reflection" made me think that you mean stray light. Can you show your solution with less wrinkeled beams and a real-size mirror? Because I actually tried my best to avoid exactly this solution.
– A. P.
2 hours ago
|
show 4 more comments
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4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
With some minor fidgeting, I'm pretty confident a setup like this can work well. Just move any unused mirror into the blue spot as shown:
answered 2 hours ago
greenturtle3141
5,22311952
Creative idea, but unfortunately mirrors are not that creative. Keeping the reflected angle the same as the incident angle, the beam has the same direction after being reflected from two parallel or orthogonal mirrors. So the downwards tendency after the inserted mirror should be the same two mirrors later.
– A. P.
2 hours ago
add a comment |
With some minor fidgeting, I'm pretty confident a setup like this can work well. Just move any unused mirror into the blue spot as shown:
answered 2 hours ago
greenturtle3141
5,22311952
Creative idea, but unfortunately mirrors are not that creative. Keeping the reflected angle the same as the incident angle, the beam has the same direction after being reflected from two parallel or orthogonal mirrors. So the downwards tendency after the inserted mirror should be the same two mirrors later.
– A. P.
2 hours ago
add a comment |
With some minor fidgeting, I'm pretty confident a setup like this can work well. Just move any unused mirror into the blue spot as shown:
answered 2 hours ago
greenturtle3141
5,22311952
With some minor fidgeting, I'm pretty confident a setup like this can work well. Just move any unused mirror into the blue spot as shown:
answered 2 hours ago
greenturtle3141
5,22311952
answered 2 hours ago
greenturtle3141
5,22311952
answered 2 hours ago
greenturtle3141
5,22311952
answered 2 hours ago
greenturtle3141
5,22311952
5,22311952
Creative idea, but unfortunately mirrors are not that creative. Keeping the reflected angle the same as the incident angle, the beam has the same direction after being reflected from two parallel or orthogonal mirrors. So the downwards tendency after the inserted mirror should be the same two mirrors later.
– A. P.
2 hours ago
add a comment |
Creative idea, but unfortunately mirrors are not that creative. Keeping the reflected angle the same as the incident angle, the beam has the same direction after being reflected from two parallel or orthogonal mirrors. So the downwards tendency after the inserted mirror should be the same two mirrors later.
– A. P.
2 hours ago
Creative idea, but unfortunately mirrors are not that creative. Keeping the reflected angle the same as the incident angle, the beam has the same direction after being reflected from two parallel or orthogonal mirrors. So the downwards tendency after the inserted mirror should be the same two mirrors later.
– A. P.
2 hours ago
Creative idea, but unfortunately mirrors are not that creative. Keeping the reflected angle the same as the incident angle, the beam has the same direction after being reflected from two parallel or orthogonal mirrors. So the downwards tendency after the inserted mirror should be the same two mirrors later.
– A. P.
2 hours ago
add a comment |
I found a solution with 2 mirrors:
answered 1 hour ago
Display name
840216
add a comment |
I found a solution with 2 mirrors:
answered 1 hour ago
Display name
840216
add a comment |
I found a solution with 2 mirrors:
answered 1 hour ago
Display name
840216
I found a solution with 2 mirrors:
answered 1 hour ago
Display name
840216
answered 1 hour ago
Display name
840216
answered 1 hour ago
Display name
840216
answered 1 hour ago
Display name
840216
840216
add a comment |
add a comment |
Assuming only 45 degree mirrors,
We are going to need two moves, and there are several ways to do it.
But since the detectors are omnidirectional, we can do better:
First take a look at the two mirrors nearest detector B. Mark the position of B' as the location of the detector B as seen through the nearest mirror. Then mark position B'', which is B', as seen through the second mirror. From that point, draw a straight line to the center of the third mirror in the very rightmost column.
Notice that the line moves 1 square sideways in 6 vertical squares. It also passes through a mirror in between. Pick up this mirror, we'll use it when we figure out where to place it.
Now, continue the line 6 squares to the left, during which time it moves 1 square up, because of the reflected angle. What joy, we are at a spot through which the original beam passes, so we can move the mirror we picked up here. We must place the mirror at an angle that is half of the beams angle ($text{arctan}(1/6) approx 9.5°$), or about 4.7 degrees, in order to hit the detector.
Like so:
answered 28 mins ago
Bass
27.1k465168
Nice explanation! rot13(Gurer vf ng yrnfg bar zber fvzvyne fbyhgvba, gurersber V jvyy jnvg fbzr gvzr orsber V npprcg gur nafjre jvgu gur uvturfg fpber.)
– A. P.
15 mins ago
add a comment |
Assuming only 45 degree mirrors,
We are going to need two moves, and there are several ways to do it.
But since the detectors are omnidirectional, we can do better:
First take a look at the two mirrors nearest detector B. Mark the position of B' as the location of the detector B as seen through the nearest mirror. Then mark position B'', which is B', as seen through the second mirror. From that point, draw a straight line to the center of the third mirror in the very rightmost column.
Notice that the line moves 1 square sideways in 6 vertical squares. It also passes through a mirror in between. Pick up this mirror, we'll use it when we figure out where to place it.
Now, continue the line 6 squares to the left, during which time it moves 1 square up, because of the reflected angle. What joy, we are at a spot through which the original beam passes, so we can move the mirror we picked up here. We must place the mirror at an angle that is half of the beams angle ($text{arctan}(1/6) approx 9.5°$), or about 4.7 degrees, in order to hit the detector.
Like so:
answered 28 mins ago
Bass
27.1k465168
Nice explanation! rot13(Gurer vf ng yrnfg bar zber fvzvyne fbyhgvba, gurersber V jvyy jnvg fbzr gvzr orsber V npprcg gur nafjre jvgu gur uvturfg fpber.)
– A. P.
15 mins ago
add a comment |
Assuming only 45 degree mirrors,
We are going to need two moves, and there are several ways to do it.
But since the detectors are omnidirectional, we can do better:
First take a look at the two mirrors nearest detector B. Mark the position of B' as the location of the detector B as seen through the nearest mirror. Then mark position B'', which is B', as seen through the second mirror. From that point, draw a straight line to the center of the third mirror in the very rightmost column.
Notice that the line moves 1 square sideways in 6 vertical squares. It also passes through a mirror in between. Pick up this mirror, we'll use it when we figure out where to place it.
Now, continue the line 6 squares to the left, during which time it moves 1 square up, because of the reflected angle. What joy, we are at a spot through which the original beam passes, so we can move the mirror we picked up here. We must place the mirror at an angle that is half of the beams angle ($text{arctan}(1/6) approx 9.5°$), or about 4.7 degrees, in order to hit the detector.
Like so:
answered 28 mins ago
Bass
27.1k465168
Assuming only 45 degree mirrors,
We are going to need two moves, and there are several ways to do it.
But since the detectors are omnidirectional, we can do better:
First take a look at the two mirrors nearest detector B. Mark the position of B' as the location of the detector B as seen through the nearest mirror. Then mark position B'', which is B', as seen through the second mirror. From that point, draw a straight line to the center of the third mirror in the very rightmost column.
Notice that the line moves 1 square sideways in 6 vertical squares. It also passes through a mirror in between. Pick up this mirror, we'll use it when we figure out where to place it.
Now, continue the line 6 squares to the left, during which time it moves 1 square up, because of the reflected angle. What joy, we are at a spot through which the original beam passes, so we can move the mirror we picked up here. We must place the mirror at an angle that is half of the beams angle ($text{arctan}(1/6) approx 9.5°$), or about 4.7 degrees, in order to hit the detector.
Like so:
answered 28 mins ago
Bass
27.1k465168
answered 28 mins ago
Bass
27.1k465168
answered 28 mins ago
Bass
27.1k465168
answered 28 mins ago
Bass
27.1k465168
27.1k465168
Nice explanation! rot13(Gurer vf ng yrnfg bar zber fvzvyne fbyhgvba, gurersber V jvyy jnvg fbzr gvzr orsber V npprcg gur nafjre jvgu gur uvturfg fpber.)
– A. P.
15 mins ago
add a comment |
Nice explanation! rot13(Gurer vf ng yrnfg bar zber fvzvyne fbyhgvba, gurersber V jvyy jnvg fbzr gvzr orsber V npprcg gur nafjre jvgu gur uvturfg fpber.)
– A. P.
15 mins ago
Nice explanation! rot13(Gurer vf ng yrnfg bar zber fvzvyne fbyhgvba, gurersber V jvyy jnvg fbzr gvzr orsber V npprcg gur nafjre jvgu gur uvturfg fpber.)
– A. P.
15 mins ago
Nice explanation! rot13(Gurer vf ng yrnfg bar zber fvzvyne fbyhgvba, gurersber V jvyy jnvg fbzr gvzr orsber V npprcg gur nafjre jvgu gur uvturfg fpber.)
– A. P.
15 mins ago
add a comment |
Possibly you could
do it with one mirror
if you
can position the mirror pointed to by the blue arrow as show below in blue in front of the mirror used by detector A and reflect directly to the detector (Thanks Dr Xorile)
Shown here
answered 2 hours ago
SteveV
5,3652629
But here you changed one of the mirrors that are used to direct the beam onto detector A.
– A. P.
2 hours ago
sorry @A.P. .i'll clear up what i meant.... rot13(chg n qvssrerag zveebe va sebag bs gur bar hfrq sbe qrgrpgbe N)
– SteveV
2 hours ago
Ok that would solve the aforementioned problem. But what I don't like about this solution is that you only direct stray light into detector B, not the whole beam. I will make this point clear in the question.
– A. P.
2 hours ago
@A.P. I'm not sure what you mean. Why would it be stray light? if they are perfect mirrors, you will get the whole beam. What i'm not sure about is if there is a gap big enough to hit the second mirror by detector B at the right angle, but thats what I'm trying! i suggest using a low power laser to check :)
– SteveV
2 hours ago
The "oblique reflection" made me think that you mean stray light. Can you show your solution with less wrinkeled beams and a real-size mirror? Because I actually tried my best to avoid exactly this solution.
– A. P.
2 hours ago
|
show 4 more comments
Possibly you could
do it with one mirror
if you
can position the mirror pointed to by the blue arrow as show below in blue in front of the mirror used by detector A and reflect directly to the detector (Thanks Dr Xorile)
Shown here
answered 2 hours ago
SteveV
5,3652629
But here you changed one of the mirrors that are used to direct the beam onto detector A.
– A. P.
2 hours ago
sorry @A.P. .i'll clear up what i meant.... rot13(chg n qvssrerag zveebe va sebag bs gur bar hfrq sbe qrgrpgbe N)
– SteveV
2 hours ago
Ok that would solve the aforementioned problem. But what I don't like about this solution is that you only direct stray light into detector B, not the whole beam. I will make this point clear in the question.
– A. P.
2 hours ago
@A.P. I'm not sure what you mean. Why would it be stray light? if they are perfect mirrors, you will get the whole beam. What i'm not sure about is if there is a gap big enough to hit the second mirror by detector B at the right angle, but thats what I'm trying! i suggest using a low power laser to check :)
– SteveV
2 hours ago
The "oblique reflection" made me think that you mean stray light. Can you show your solution with less wrinkeled beams and a real-size mirror? Because I actually tried my best to avoid exactly this solution.
– A. P.
2 hours ago
|
show 4 more comments
Possibly you could
do it with one mirror
if you
can position the mirror pointed to by the blue arrow as show below in blue in front of the mirror used by detector A and reflect directly to the detector (Thanks Dr Xorile)
Shown here
answered 2 hours ago
SteveV
5,3652629
Possibly you could
do it with one mirror
if you
can position the mirror pointed to by the blue arrow as show below in blue in front of the mirror used by detector A and reflect directly to the detector (Thanks Dr Xorile)
Shown here
answered 2 hours ago
SteveV
5,3652629
edited 1 hour ago
answered 2 hours ago
SteveV
5,3652629
answered 2 hours ago
SteveV
5,3652629
answered 2 hours ago
SteveV
5,3652629
5,3652629
But here you changed one of the mirrors that are used to direct the beam onto detector A.
– A. P.
2 hours ago
sorry @A.P. .i'll clear up what i meant.... rot13(chg n qvssrerag zveebe va sebag bs gur bar hfrq sbe qrgrpgbe N)
– SteveV
2 hours ago
Ok that would solve the aforementioned problem. But what I don't like about this solution is that you only direct stray light into detector B, not the whole beam. I will make this point clear in the question.
– A. P.
2 hours ago
@A.P. I'm not sure what you mean. Why would it be stray light? if they are perfect mirrors, you will get the whole beam. What i'm not sure about is if there is a gap big enough to hit the second mirror by detector B at the right angle, but thats what I'm trying! i suggest using a low power laser to check :)
– SteveV
2 hours ago
The "oblique reflection" made me think that you mean stray light. Can you show your solution with less wrinkeled beams and a real-size mirror? Because I actually tried my best to avoid exactly this solution.
– A. P.
2 hours ago
|
show 4 more comments
But here you changed one of the mirrors that are used to direct the beam onto detector A.
– A. P.
2 hours ago
sorry @A.P. .i'll clear up what i meant.... rot13(chg n qvssrerag zveebe va sebag bs gur bar hfrq sbe qrgrpgbe N)
– SteveV
2 hours ago
Ok that would solve the aforementioned problem. But what I don't like about this solution is that you only direct stray light into detector B, not the whole beam. I will make this point clear in the question.
– A. P.
2 hours ago
@A.P. I'm not sure what you mean. Why would it be stray light? if they are perfect mirrors, you will get the whole beam. What i'm not sure about is if there is a gap big enough to hit the second mirror by detector B at the right angle, but thats what I'm trying! i suggest using a low power laser to check :)
– SteveV
2 hours ago
The "oblique reflection" made me think that you mean stray light. Can you show your solution with less wrinkeled beams and a real-size mirror? Because I actually tried my best to avoid exactly this solution.
– A. P.
2 hours ago
But here you changed one of the mirrors that are used to direct the beam onto detector A.
– A. P.
2 hours ago
But here you changed one of the mirrors that are used to direct the beam onto detector A.
– A. P.
2 hours ago
sorry @A.P. .i'll clear up what i meant.... rot13(chg n qvssrerag zveebe va sebag bs gur bar hfrq sbe qrgrpgbe N)
– SteveV
2 hours ago
sorry @A.P. .i'll clear up what i meant.... rot13(chg n qvssrerag zveebe va sebag bs gur bar hfrq sbe qrgrpgbe N)
– SteveV
2 hours ago
Ok that would solve the aforementioned problem. But what I don't like about this solution is that you only direct stray light into detector B, not the whole beam. I will make this point clear in the question.
– A. P.
2 hours ago
Ok that would solve the aforementioned problem. But what I don't like about this solution is that you only direct stray light into detector B, not the whole beam. I will make this point clear in the question.
– A. P.
2 hours ago
@A.P. I'm not sure what you mean. Why would it be stray light? if they are perfect mirrors, you will get the whole beam. What i'm not sure about is if there is a gap big enough to hit the second mirror by detector B at the right angle, but thats what I'm trying! i suggest using a low power laser to check :)
– SteveV
2 hours ago
@A.P. I'm not sure what you mean. Why would it be stray light? if they are perfect mirrors, you will get the whole beam. What i'm not sure about is if there is a gap big enough to hit the second mirror by detector B at the right angle, but thats what I'm trying! i suggest using a low power laser to check :)
– SteveV
2 hours ago
The "oblique reflection" made me think that you mean stray light. Can you show your solution with less wrinkeled beams and a real-size mirror? Because I actually tried my best to avoid exactly this solution.
– A. P.
2 hours ago
The "oblique reflection" made me think that you mean stray light. Can you show your solution with less wrinkeled beams and a real-size mirror? Because I actually tried my best to avoid exactly this solution.
– A. P.
2 hours ago
|
show 4 more comments
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Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
