Optical Flat - How Interference Fringes Form

How Interference Fringes Form

See diagram (right). The upper object is a section of the optical flat, the lower object a section of the test surface it is resting on. Unless the two surfaces are exactly flat and parallel, there will be a tiny gap between them. Monochromatic light (red) shines through the glass flat and reflects from both the bottom surface of the flat and the top surface of the test flat, and the two reflected rays combine and superpose. However the ray reflecting off the bottom surface travels a longer path. The additional path length is equal to twice the gap between the surfaces.

• Constructive interference: At surface locations (b) where the path length difference between the two rays is equal to an even multiple of half a wavelength (λ/2) of the light waves, the reflected waves will be in phase, so the "troughs" and "peaks" of the waves coincide. Therefore the waves will reinforce (add) and the resulting light intensity will be greater. As a result a bright area will be observed there.
• Destructive interference: At other locations (a) where the path length difference is equal to an odd multiple of a half-wavelength, the reflected waves will be 180° out of phase, so a "trough" of one wave coincides with a "peak" of the other wave. Therefore the waves will cancel (subtract) and the resulting light intensity will be weaker or zero. As a result a dark area will be observed there.

If the gap between the surfaces is not constant, this interference results in a pattern of bright and dark lines or bands called "interference fringes" being observed on the surface. These are similar to contour lines on maps, revealing the height differences of the bottom test surface. The gap between the surfaces is constant along a fringe. The path length difference between two adjacent bright or dark fringes is one wavelength of the light, so the difference in the gap between the surfaces is one-half wavelength.