294 ILLINOIS STATE ACADEMY OF fe^IENCE 



A METHOD OF MAGNIFYING SMALL ANGULAR 

 DISPLACEMENTS 



Ralph C. Hahtsough, Illinois Wesleyan Uniteesity 

 outline and summaey 



1. Basic principle is multiple reflection 

 11. Limits of range 



(a) Theoretical 



(b) Practical 



III. Experimental data and conclusions. 



SUMMARY 



By multiple reflection between two parallel mirrors, an 

 incident ray is turned through a magnified angle upon 

 emerging provided one or both of the mirrors are turned 

 slightly. The amount of magnification depends on the 

 number of reflections. Theoretically the limits of opera- 

 tion are much greater than are possible from a prac- 

 tical standpoint, for on account of absorption, the inci- 

 dent ray after many reflections becomes a very weak 

 emergent ray. However, with mirrors of high reflective 

 power, and by taking advantage of moving both mirrors, 

 a magnification of one hundred is easily obtainable. 



I. BASIC principle IS MULTIPLE REFLECTION 



The author was confronted with the problem of mea- 

 suring some very small angular displacements, and de- 

 vised an optical method which he chose to call ''The 

 angleometer". A beam of light is reflected back and 

 forth between two parallel mirrors as in Figure I. If 

 either or both of the mirrors are turned through a small 

 angle, the emergent ray will be turned through an in- 

 creased angle depending upon the number of reflections 

 of the turning mirror. 



In Figure I, the illustration shows the short mirror 

 stationary, and the long mirror turning through a small 

 angle. The number of reflections on the movable mirror 

 multiplied by two gives the magnification number. A 

 reflected ray from a mirror is turned through twice the 



