Testing for Flatness
Testing for Flatness. Plane surfaces are tested for flatness by placing two polished surfaces together and observing the interference bands that appear between them when viewed under monochromatic light. The surfaces must be clean and free of all grease and dust or the bands may not show up.
Because of its wave nature, light reflected from the surfaces
under test alternately reinforces and interferes with itself, interference occurring with each successive half wave length of separation of the surfaces, which points are marked by the presence of
dark bands, or fringes. These bands can be interpreted just as are the contour lines on a topographic map, where the terrain along any given line is all of the same elevation.
For example, the surfaces in Fig. 52 are, anywhere along band 2, a half wave length farther apart than they are along band 1; anywhere along band 3 they are a half wave farther apart than along band 2, and so on. Flat surfaces, A in the diagram, or spherical surfaces of equal radii, B, present identical band patterns.
The direction of greatest separation, or the direction of the wedge opening, can be found by pressing at one side or the other. Pressing at the left tilts the top piece at a steeper angle, widening the wedge opening, and as more bands move in they become thinner and more closely spaced. Pressing at the right, at x, narrows the wedge opening; as the bands move out they become broader and fewer in number until only one band, spread out across the whole specimen, may be seen when the
surfaces have been brought parallel to each other.
Where one or both surfaces are not flat, curved bands may be seen, resembling the appearance in Fig. 52C. A little reasoning will show that, by placing a straightedge along the bands, as indicated by the dotted line, and counting their number intersected by it, the amount of convexity (or concavity) can be determined. At C, three bands are cut through, hence the surfaces are either convex or concave to each other by l½ wave lengths. The changing band appearance under appropriate pressure will disclose which is the case.
By pressing at the right, at x, narrowing the wedge opening, the bands (in this case) will move off in that direction, and the bull's-eye, or center of the fringe system, will
come into view, having the appearance of Fig. 53c (where the same specimens are again tested). The departure from flatness can then be determined by counting the number of rings visible; in this case three rings are present, hence the surfaces are 1½ waves off.
Note that the bull's-eye, in the case of convexity at the point of contact, moves toward the point of pressure. Or, if convexity is so slight that the bull's-eye is not in evidence, the curved bands, convex toward the wedge opening, move, convex, toward that point when pressure is applied there. In the case of concavity, the
bull's-eye would mark the point of widest separation of the surfaces, and in that case, application of pressure at the center would cause the rings to flow inward and to become fewer in number; the bull's- eye would recede from a point of pressure at any edge.
With only curved bands showing, as in Fig. 52C, the wedge opening, with concavity, would be at the left; by applying pressure there to narrow the wedge, the bands, concave toward that point, would move in that direction and become fewer in number. By these means, the relationship of the contacting surfaces to one another is easily determined. In commercial optics, surfaces are tested against a master flat of known precision, so the exact condition of a specimen is immediately known.
Although you may have no master flat, you require only three specimens of good plate glass and a little elementary algebra to measure with equal accuracy the flatness of a surface of each specimen. A hypothetical problem is illustrated in Fig. 53, for three pieces of glass marked A, B, and C. Placing A on B, we get the pattern of bands shown at a, one band convex. B on C gives the pattern at b, eight bands convex. A on C results in the pattern at c, three bands convex. (When
making an actual test, several minutes should be allowed to elapse before writing down each result, as heat from the hands will introduce temporary errors.) Convexity is usually assumed to be positive (plus), and concavity negative (minus), so the following simultaneous equations may be written:
A + B=+l; B + C=+8; A + C=+3.
Solve the first equation for B and substitute the result, 1~A,
in the second equation. This gives two equations:
A - C= -7, and A + C = + 3.
Solve the first equation above for A and substitute the result,
C — 7, in the last equation, whence 2C = +10.
From this solution, C = + 5, B ~ +3, and A = — 2. Remembering that from one band to the next represents a difference in surface separation of ½ wave length, then
A = — 2 bands, or 1 wave concave,
B = + 3 bands, or 1½ waves convex,
C= +5 bands, or 2½ waves convex
next- making the diagonal
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