JOURNAL OF COSMETIC SCIENCE 98 The fi rst step is to use equation 13 to determine the pathlength difference of the fi lm: 2 × 2.5 × 255 × Cos(0) = 1275 nm. Next, the intensities of various wavelengths need to be determined and plotted. For this ex- ample, the intensities for the primary colors, 450 nm, 550 nm, and 650 nm are worked out. Figure 21. Primary color intensities (blue, green, red) for the 155-nm fi lm, plus other wavelengths to fi ll out the green spectral curve. Figure 22. Interference color progression for a fi lm starting at 60 nm (red square) and stepping every 5 nm. Figure 20. Primary color intensities (blue, green, red) for the 120-nm fi lm, plus other wavelengths to fi ll out the blue spectral curve.

BASIC OPTICS OF EFFECT MATERIALS 99 Starting with 450 nm, fi rst determine the phase shift by taking 2π/λ × pathlength and adding π for constructive interference: ( / , / .9440 2 450 360 2 20 π π π × 1275) × + = = 20.9440 radians 1200 degrees or Next the result of interference is calculated and plotted. Table I contains the calculation and Figure 23 shows the plot for 450 nm. The amplitude of the resulting wave is the maximum magnitude, which in this example is at 150 degrees. Since the value at 150 degrees was not previously calculated, it is calculated here: Amplitude Sin(150) Sin(150 1200) 1.00 = + − = The intensity, which is the square of the amplitude, equals (1.00)2 = 1.00. Similarly, with 550 nm, fi rst determine the phase shift by taking 2π/λ × pathlength and adding π for constructive interference: ( / / .7072 2 1275) 360 2 17 1015 π π π 550 17.7072 radians or, degrees × × + = = Again, the result of interference is calculated and plotted. Table II contains the calcula- tion and Figure 24 shows the plot for 550 nm. The amplitude of the resulting wave is the Figure 23. Calculated result of interference at 450 nm. Table I Calcuation for 450 nm x y = sin(x) y = sin(x-1200) Sum 0 0 −0.86603 −0.86603 45 0.7071 −0.96593 −0.25882 90 1 −0.5 0.5 135 0.7071 0.258819 0.965926 180 0 0.866025 0.866025 225 −0.7071 0.965926 0.258819 270 −1 0.5 −0.5 315 −0.7071 −0.25882 −0.96593 360 0 −0.86603 −0.86603