what visible wavelengths of light are strongly reflected from a 390-nm-thick soap bubble?

what visible wavelengths of light are strongly reflected from a 390-nm-thick soap bubble?

The shades we see in the bubble are produced by the disturbance in between 2 waves: a) the wave reflected by the surface of the bubble b) the wave that travels inside the bubble and it's reflected by its back.
The problem for the useful disturbance is that the stage shift in between both waves is an integer several of. The stage distinction in between both waves is

where is two times the density of the bubble (since the second wave travels inside the bubble and it's reflected from the back), while is because of that the first wave has an extra stage shift because it's reflected from a material (soap) with greater refraction index compared to the air.

So, in purchase to have useful disturbance, we should require

where m is an integer. Replacing and , we have

But here is the wavelength in the soap; we need rather the wavelength airborne, which is

where n=1.33 is the refraction index.

Therefore, we have


Using t=390 nm, and using various worths of m, we find tha just m=1 and m=2 have wavelength in the noticeable range: and. These wavelengths represent red and violet, so the bubble shows up as red-violet.
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