Find the minimum thickness (in nm) of a soap bubble that appears red when illuminated by white light perpendicular to its surface. Take the wavelength to be 680 nm, and assume the same index of refraction as water.

We need to find the minimum thickness of a soap bubble that appears red when illuminated by white light perpendicular to its surface. Let t is the minimum thickness of the film. When reflection is taking place at an interface, then the condition for constructive interference is given by :

[tex]2t=\dfrac{\lambda}{2}\\\\t=\dfrac{\lambda}{4}\\\\t=\dfrac{680\times 10^{-9}}{4}\\\\t=1.7\times 10^{-7}\ m\\\\t=170\ nm[/tex]

So, the thickness of the soap bubble is 170 nm.

tallinn tallinn · Answer 2 · 2022-04-12T15:22:43+02:00

When the wavelength is 680 nm and assumes the same index of refraction as water So, The thickness of the soap bubble is 170 nm.

What is the Index of Refraction?

Given that as the per question,

Then, The Wavelength of light, [tex]\lambda = 680nm[/tex]

Now, We are required to find the minimum thickness of a soap bubble that appears red when illuminated by white light perpendicular to its surface.

Then, Let t be the minimum thickness of the film.

When The reflection is taking place at an interface, then the condition for constructive interference is given by:

[tex]2t = \lambda/2[/tex]

[tex]t = \lambda/4[/tex]

t is = 680×10⁻⁹/4

t is = 1.7 ˣ 10⁻⁷ m

Therefore, t = 170 nm

Hence, When the thickness of the soap bubble is 170 nm.

Find more information about Index of Refraction here:

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