Question

A soap bubblefilm that is 106 nm thick and has an index of refraction of 1.42 results in constructive interference in the reflected light if this film is illuminated by a beam of light with a wavelength of 601 nm. What are the next three thicknesses of this film that will also result in constructive interference?

Answer 1

Constructive interference in soap bubble films occurs at certain film thicknesses based on the interference formula. For a soap bubble with index of refraction 1.42 and light wavelength of 601 nm, the next three thicknesses can be calculated by incrementing the order of interference in the formula for constructive interference.

Step-by-step explanation:

The question asks about finding subsequent thicknesses of a soap bubble film that result in constructive interference of reflected light at a given wavelength and index of refraction. Constructive interference in thin films such as soap bubbles occurs when the path difference between two rays reflected from the top and bottom surfaces of the film is equal to an integer multiple of the wavelength in the medium, or an odd multiple of half-wavelengths adjusted for any phase shifts that occur upon reflection. In this case, the phase shift happens upon reflection from the denser medium, leading to an additional half-wavelength path difference.

To find the thicknesses that will result in constructive interference, the formula 2
t = (m + 1/2)λ/n can be used, where
t is the thickness of the film,
λ is the wavelength of light in a vacuum, n is the index of refraction of the film, and m is an integer number representing the order of the interference fringe. We can solve for the next three values of t by incrementing m, given that one thickness already known to cause constructive interference is 106 nm.