Two glass plates are separated by fine wires with monochromatic light with diame

Question

Two glass plates are separated by fine wires with monochromatic light with diameters d_2 = 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 700 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

given

d1 = 0.0500 mm

and

d2 = 0.0520 mm

L = 7.00 cm

= 564nm

( 2 d / ) + 1 / 2 = n

dn = ( m - 1/2 ) / 2

to get y value

using equation

y = dn+1 - dn

y = ( ( m + 1 - 1/2 ) / 2 - ( m - 1/2 ) / 2

y = / 2

to get slope value

slope = d2 - d1 / L

slope = 0.0520 - 0.050 / 7

slope = 2.91 X 10-4 mm /cm

to get the distance (in cm) between adjacent dark bands in the reflected light value is x

then x = y / slope

x = / 2 / 2.91 X 10-4

x = 0.5 X 564 X 10-9 X 10-6 / 2.91 X 10-4

x = 0.969 cm------ans

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