Foucault Theory
Theory of the Foucault Test. This method of testing a concave reflecting surface was devised by Jean Foucault, of pendulum fame. The impressive features of this test are its simplicity and extreme sensitivity. Foucault's theory was that if an artificial star
(illuminated pinhole) be placed at the center of curvature of a
spherical mirror, then all of the rays from it that fall upon the
surface of the mirror will be perpendicular thereto and, by the law of reflection, will be returned along the same paths, to form an image of the pinhole on the pinhole itself.
Of course, the image could not be examined in this position, but if the pinhole were shifted to one side (we shift it to the right), the image would be shifted a corresponding distance to the other. Now if a knife-edge be cut into this image at right angles, all of the rays will be at once intercepted, and if the illuminated mirror were being viewed by the eye as shown in Fig. 21a, it would appear to darken instantly. But if the curve on the mirror deviates the slightest amount from a true spherical figure, then all of the rays will not intersect in that pinhole image. Instead, rays^ from those zones of different curvature will intersect in slightly separated points along the axis of the reflected cone of light.
One such variation of surface curvature is shown in Fig. 21b. Here, the knife-edge could nowhere be placed so as to intercept all of the rays at once, and to the eye viewing the mirror, those parts from which rays had been intercepted would appear dark, while the other parts would still appear illuminated. By exploring along a small range of the axis of the cone with the knife-edge, and measuring the distance between the points of intersection of these radii, it is possible to tell what our curve is, almost to the millionth part of an inch.
MIRROR MATERIALS CHECK LIST
Item Quantity
1. 6-inch pyrex mirror blank 1
2. 6-inch plate-glass disk 1
3. Abrasives:
Carborundum # 80 8 oz.
#120 3 oz.
#220 1 oz.
#400 1 oz.
Alundum #600 or #2 garnet powder ½ oz.
Emery #305 or #8 garnet powder ½ °z-
4. Polishing agent:
Rouge, cerium oxide, or Barnesite
5. For the lap:
Pitch 1 lb
Rosin ½ lb
Beeswax 2 oz.
6. Miscellaneous items:
Water pail 1
Water bottle or shaker 1
Carborundum stone (coarse & fine) 1 ea.
Turpentine
Paraffin
Small paint brush 1
Magnifying lens (eyepiece) 1
Small pot 1
Empty cans 3
Hot plate or gas burner 1
(kitchen stove will do)
7. To make or improvise:
Template 1
Channeling tool (or rubber mold) 1
Grinding stand or barrel 1
Foucault testing device 1
Testing rack 1
Stands for testing device and rack 1 ea
The various grades of abrasive listed opposite are by no means the only sizes that may be used. The transformation of the mirror's surface from a coarsely pitted one to the satin-like finish requisite for quick and complete polishing can be made with any series of progressively smaller grain sizes. It is expensive and time consuming to encumber the operation with many different grades, and yet
if too large a gap exists between the various sizes, an undue length of time will have to be spent with each one.
Hand grinding of a Pyrex mirror is perhaps most efficiently accomplished with not fewer than six judiciously chosen grades. Use of a larger number is not necessarily a greater assurance of success, however, as there have
been many instances where, with as many as 12 different sized abrasives being used, coarse pits still remained, and the last few stages
had to be repeated.
It is not absolutely essential that the plate-glass tool be of the thickness recommended on page 27, but the thickness should never be less than 1/12 the diameter. For unless the surfaces of both tool and barrel top match quite perfectly, such a thin tool might yield slightly under the pressure of grinding, or the weight of cold pressing when polishing, and it would be difficult to maintain a surface of revolution. In any upside-down grinding, a thin tool is sure to
bend under the pressure, and a spherical surface under these conditions is almost an impossibility. In considering the matter of thickness, see Chapter VII for further uses to which the tool may be put.
Chapter 3 Mirror Grinding
