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What is the thinnest soap film (excluding the case of zero thickness) that appears black when illuminated with light with a wavelength of 515 nm ? The index of refraction of the film is 1.32, and there is air on both sides of the film.
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for destructive interference (appears black)
2 t = m ? / u (where m = 0 1 2 3 ... is order of minima)

where t = tickness, u = ref index = 1.35
? = 490*10^-9 meter
for t (minimum) m = 1 (as m=0 is ruled out as t>0)
t = 1* 515*10^-9/2*1.32
t (min) = 195.076*10^-9 meter OR
t (min) = 0.195*10^-6 meter = 0.195 micro meter (ans)
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