Two glass pates are separated by fine wires with diameters d_1 = 0.0500 mm and d

Question

Two glass pates are separated by fine wires with diameters d_1 = 0.0500 mm and d_2 = 0.0520 mm, as indicated in the figure (Figure 1). The wires are parallel and separated by a distance of 7.00 cm. If monochromatic light with lambda = 564 nm is incident from above, what is the distance (in cm) between adjacent dark bands in the reflected light? (Consider interference only between light reflected from the bottom surface of the upper plate and light reflected from the upper surface of the lower plate.)

Explanation / Answer

D1 = 0.05 mm = 0.05 * 10-3 m, D2 = 0.052 * 10-3 m

Distance between wires = 7 * 10-2 m, wavelength = 564 * 10-9 m

slope of glass plate = (0.052 - 0.050) * 10-3 / 7 * 10-2 = 2.86 * 10-5 m

Length of bands a = (0.052 * 10-3) / (2.86 * 10-5 ) = 1.82 m

Number of dark bands m = 2d / lambda = (2 * 0.052 * 10-3) / (564 * 10-9) = 184 dark bands

Distance = 1.82 / 184

= 9.87 * 10-3 m

= 0.987 cm

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