Passage 6: Soap
Soap bubbles, despite their delicate and transient nature, have fascinated scientists
and laypeople alike for hundreds of years. When passing a white light source
through a soap bubble, a series of colorful bands can be observed along the surface
which changes with thickness of the soap film.
Scientists studying this phenomenon came up with an experiment to investigate
this behavior of light and physical properties of the soap bubbles themselves.
Materials:
• Soap solution
• White light source
• Camera with infrared, visible, and UV filters
• Spectrometer
• Polarizing filters
Procedure:
First, a soap solution was prepared with water, a small amount of soap, and glycerin.
The presence of glycerin was helpful to counter a primary limiting factor for the
stability of soap bubbles: surface tension. The bubbles were then illuminated with
the white light source, and the infrared, visible, and UV camera filters were used to
capture images of the three spectra.
Interference patterns were recorded as the bubbles expanded. Spectrometry was
utilized to analyze the light that was both reflected and transmitted through the film
at different angles. Results are tabulated below.
By the end of the experiment, the researchers concluded that the interference
patterns had the most observable effect on the vibrance of colors in the visible
spectrum. Infrared radiation was largely absorbed, but UV light experienced
significant scattering. When viewed through the polarizing filters, intensity of light
varied consistently with the orientation of the polarizer.
During this experiment, the researchers observed a reflected dominant
wavelength of 600nm at normal incidence (0 degrees) in one soap bubble. The
refractive index of the film is 1.33, and the refractive index of air is 1.0. What is
the minimum thickness of soap film that can reflect this wavelength of light
due to constructive interference? Assume a π phase shift upon reflection from
the air-soap film interface.
A) 113 nm
B) 226 nm
C) 300 nm
D) 600 nm
Correct answer: A. When dealing with constructive interference in
a thin-film interference scenario, the path difference (2t) is equal to an integer
multiple of the wavelength in the film (adjustments made for phase shifts). This
question asks you to assume that there is a π shift at the air-soap interface, but not
at the soap-air interface (meaning that there is a π shift when light from the outside
hits the soap film, but not when it leaves the soap film, going through to the inside
of the bubble). This is because the refractive index of the soap film is higher than
that of air (1.33 vs 1.0). Thus, this scenario entails a half-wavelength shift:
2nt = (m+1/2)λ → equation for constructive interference in a thin film with one reflection
causing a π shift, where n is the refractive index of the film, t is the thickness of the film,
m is the order of interference, and λ is the wavelength of the light.
Since minimum thickness of the film is our objective, we can assume m=0, so our
equation simplifies to:
t = λ/4n
Solving for t (our thickness), we get approximately 112.78nm, so A is the answer.
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