The Lazy Laser Physicist












4
















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







share|improve this question





























    4
















    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







    share|improve this question



























      4












      4








      4









      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







      share|improve this question

















      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






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited 2 hours ago

























      asked 3 hours ago









      A. P.

      3,20011041




      3,20011041






















          4 Answers
          4






          active

          oldest

          votes


















          2














          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:




          idk







          share|improve this answer





















          • 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



















          1














          I found a solution with 2 mirrors:




          enter image description here







          share|improve this answer





























            1














            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:




            enter image description here







            share|improve this answer





















            • 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.
              26 mins ago



















            0














            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




            enter image description here







            share|improve this answer























            • 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











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            4 Answers
            4






            active

            oldest

            votes








            4 Answers
            4






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            2














            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:




            idk







            share|improve this answer





















            • 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
















            2














            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:




            idk







            share|improve this answer





















            • 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














            2












            2








            2






            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:




            idk







            share|improve this answer












            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:




            idk








            share|improve this answer












            share|improve this answer



            share|improve this answer










            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


















            • 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











            1














            I found a solution with 2 mirrors:




            enter image description here







            share|improve this answer


























              1














              I found a solution with 2 mirrors:




              enter image description here







              share|improve this answer
























                1












                1








                1






                I found a solution with 2 mirrors:




                enter image description here







                share|improve this answer












                I found a solution with 2 mirrors:




                enter image description here








                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered 1 hour ago









                Display name

                840216




                840216























                    1














                    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:




                    enter image description here







                    share|improve this answer





















                    • 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.
                      26 mins ago
















                    1














                    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:




                    enter image description here







                    share|improve this answer





















                    • 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.
                      26 mins ago














                    1












                    1








                    1






                    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:




                    enter image description here







                    share|improve this answer












                    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:




                    enter image description here








                    share|improve this answer












                    share|improve this answer



                    share|improve this answer










                    answered 39 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.
                      26 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.
                      26 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.
                    26 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.
                    26 mins ago











                    0














                    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




                    enter image description here







                    share|improve this answer























                    • 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
















                    0














                    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




                    enter image description here







                    share|improve this answer























                    • 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














                    0












                    0








                    0






                    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




                    enter image description here







                    share|improve this answer














                    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




                    enter image description here








                    share|improve this answer














                    share|improve this answer



                    share|improve this answer








                    edited 2 hours ago

























                    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


















                    • 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


















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