I have a soap film (index of refraction 1.33) which is illuminated by light of w

Question

I have a soap film (index of refraction 1.33) which is illuminated by light of wavelength 480 nm. What is the smallest thickness of the film that would appear black? (there is air on both sides of the soap film) What are two other possible thicknesses of the film that would also appear black? I have a soap film (index of refraction 1.33) which is illuminated by light of wavelength 480 nm. What is the smallest thickness of the film that would appear black? (there is air on both sides of the soap film) What are two other possible thicknesses of the film that would also appear black?

Explanation / Answer

given

n = 1.33

lamda = 480 nm

let t is the minimum thickness of soap film that would appear black.

let t is the minimum thickness.

2*t = lamda/(2*n)

t = lamda/(4*n)

= 480*10^-9/(4*1.33)

= 90.2 nm or 9.02*10^-8 m

when the thickness is 3*t,5*t, 7*t.... also the film would appear black.

t2 = 3*90.2 = 270.6 nm = 2.706*10^-7 m

t3 = 5*90.2 = 451 nm = 4.51*10^-7 m

t4 = 7*90.2

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