How do I measure an unknown distance using mirrors and not doing any direct measurement?

Question

I've tried lasers but they do not work out and i am very confused with the mirror idea. How can I use two mirrors to find the unknown distance between two objects? Can you please give a procedure? thanks

please note that there can be no direct measurement. All the measurements must be done before hand but there will be no measurements allowed at the time of the presentation. Calculations are allowed

what is meant by direct measurement is time, rulers, etc...

Answer 1

On the two distant objects (points B & C) place your mirrors one on each object facing each other at complimentary 45 drgree angles to the line BC. If you shine a light at mirror B it will reflect at its angle if incidence to the mirror. As you change the angle of the light you will eventually bounce the light off mirror B so that it strikes mirror C. There will be a point where you will be able to bounce the light off Mirror B so that I strikes Mirror C in such a way that the light returns to its origin at a 90 degree angle.

Con gratulations you have just found point A of trinangle BAC with the following angles (45 90 45) .

Next shine the light at a mirror so that is angle of incidence = 0. Basically shine directly back at you. You now have a bearing to that mirror. Repeat this for the other mirror and you will have two intersecting lines. The interscetion of which is point D . You now have a second triangle BDC with the angles (22.5 135 22.5)

You can also now measure a distance AD which will have a complimentary distance A'D where A' should be the midpoint between the two mirrors.

If you draw this out you will see that you will have enough information to use trigonometery to solve a couple of right triangles .

Answer 2

You could set the mirrors up so that when looking at mirror A from object A, you see mirror B, which itself has an image of object B.

You need to know the distance from object A to mirror A, the angle of the mirror A relative to a line connecting object A and B, the distance from mirror B to object B, and its angle relative to this line also. You then can plot all these on graph paper to get a good idea of the distance between object A and object B (could use trigonometry as well).

There are probably many ways to set the mirrors up, but I think this is what the instructor is trying to get you to do, to use geometry and trigonometry to find the distance.

A different arrangement is to use the mirrors separately. Place each mirror so that object B can be seen from object A. Measure the distance from each mirror to object A, and the distance from each mirror to an imaginary line connecting A and B. (The mirrors should preferably be on opposite sides of a line connecting A and B.) Measure also the angle of the mirror relative to a line connecting A and B. Do this for both mirrors. This would give you two angles to plot on graph paper (one for each mirror). Two mirrors in this type of setup are needed (correction from earlier), because each measurement would give only a line on which object B is found, but no information as to its distance. The intersection of the two plotted lines would be the location of object B.

Answer 3

ru Engineering student ?
in survery particel using plane table method of measuring in accessable distance . plz check dip., BE Civil engineering survey books . bye