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(A) (B)
Fig. 1. Interference effects in single 4 X films on glass.
refraction higher than that of glass, while the film in diagram (b) has an index of refraction lower than that of glass.
Any light ray incident on such a film becomes the source of two sets of almost superimposed parallel rays. These rays tend to cancel or reinforce each other by destructive or constructive interference. The type of interference which occurs depends on the relative phase of the interfering rays. The phase of the reflected and transmitted rays is determined by the optical path through the film and by phase reversals which occur on reflection from a denser medium. In these diagrams, phase is indicated by solid and broken line segments. For simplicity, the angle of refraction is ignored.
The high-index film produces reinforcement for a specified wavelength in the reflected light and cancellation in the transmitted light. Here, the only phase change due to reflection from a denser medium occurs at the air-film boundary.
The successive rays, proceeding toward the right, are less and less intense ; hence the effects of the first two reflected rays, and the first two transmitted rays, are dominating. The phase reversal of alternate succeeding rays modifies the effect of the first two rays, therefore neither cancellation nor reinforcement is complete.
In the low-index film, there is a phase
change in the initial reflection from the air-film boundary and at each reflection from the film-glass boundary. As a result, an effective film thickness equal to J of the wavelength here produces cancellation in the reflected light and reinforcement in the transmitted light.
The amplitude of the reflected rays, for a specified angle of incidence, is determined by the relative indices of refraction of the materials on either side of the boundary from which reflection occurs. Therefore, if the relative indices of refraction of the air, film and glass were of such value that the amplitude of the ray initially reflected at the airfilm boundary equalled the sum of the amplitudes of the other reflected rays, no light of the specified wavelength would be reflected from the film in diagram (B), since the rays are 1 80° out of phase.
The maximum reflectance obtainable from a single film is determined by the index of refraction of the film. In order to increase the reflectance for a certain wavelength, multiple alternate layers of high and low-index materials are applied. The film thickness for each layer is controlled so that the initial reflected rays, of the control wavelength, from each film boundary are in phase when they leave the film. The reflected intensity for that wavelength is then equal to the square of the sum of the amplitudes of the reflected rays.
A diagram representing a seven-layer
358
April 1953 Journal of the SMPTE Vol.60