What is the thinnest soap film (excluding the case of zero thickness) that appea

Question

What is the thinnest soap film (excluding the case of zero thickness) that appears black when illuminated with light with a wavelength of 570nm ? The index of refraction of the film is 1.34, and there is air on both sides of the film. Express your answer in nanometers. What is the thinnest soap film (excluding the case of zero thickness) that appears black when illuminated with light with a wavelength of 570nm ? The index of refraction of the film is 1.34, and there is air on both sides of the film. Express your answer in nanometers.

Explanation / Answer

for destructive interference (appears black)
2 t = m ÃŽ » / u (where m = 0 1 2 3 ... is order of minima)

where t = tickness, u = ref index = 1.34
ÃŽ » = 570*10^-9 meter
for t (minimum) m = 1 (as m=0 is ruled out as t>0)
t = 1* 570*10^-9/2*1.35
t (min) = 212.57*10^-9 meter OR
t (min) = 0.212*10^-6 meter = 0.212 micro meter

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