Question

In: Physics

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

A soap bubble is essentially a thin film of water surrounded by air. The colors you see in soap bubbles are produced by interference. What visible wavelengths of light are strongly reflected from a 390-nm-thick soap bubble? What color would such a soap bubble appear to be?

Solutions

Expert Solution

For \(m=0\), the wavelength

$$ \lambda=\frac{4 n t}{1} $$

Substitute 1.33 for \(n\) and \(390 \mathrm{nm}\) for \(t\)

$$ \begin{aligned} \lambda &=\frac{4(1.33)\left(390 \mathrm{nm}\left(\frac{1 \mathrm{~m}}{10^{9} \mathrm{nm}}\right)\right)}{1} \\ &=2074.8 \mathrm{nm} \end{aligned} $$

For \(m=1,\) the visible wavelength

$$ \begin{aligned} \lambda &=\frac{4(1.33)\left(390 \mathrm{nm}\left(\frac{1 \mathrm{~m}}{10^{9} \mathrm{nm}}\right)\right)}{3} \\ & \approx 690 \mathrm{nm} \end{aligned} $$

For \(m=2,\) the visible wavelength

$$ \begin{aligned} \lambda &=\frac{4(1.33)\left(390 \mathrm{nm}\left(\frac{1 \mathrm{~m}}{10^{9} \mathrm{nm}}\right)\right)}{5} \\ &=414.96 \mathrm{nm} \\ & \approx 410 \mathrm{nm} \end{aligned} $$

For \(m=3,\) the wavelength

$$ \begin{aligned} \lambda &=\frac{4(1.33)\left(390 \mathrm{nm}\left(\frac{1 \mathrm{~m}}{10^{9} \mathrm{nm}}\right)\right)}{7} \\ &=296.4 \mathrm{nm} \end{aligned} $$

Values of \(m\) greater than 3 lead to values of \(\lambda\) that are smaller than \(296.4 \mathrm{nm} .\) Thus the wavelengths in the visible spectrum \((400-700 \mathrm{nm})\) that are strongly reflected by the film are \(410 \mathrm{nm}\) and \(690 \mathrm{nm}\)

Hence, the soap bubble would appear purple due to the combination of deep violet \((410 \mathrm{nm})\) and red \((690 \mathrm{nm})\).


the soap bubble would appear purple due to the combination of deep violet \((410 \mathrm{nm})\) and red \((690 \mathrm{nm})\).

Related Solutions

A soap bubble is 95 nm thick and illuminated by white light incident perpendicular to its...
A soap bubble is 95 nm thick and illuminated by white light incident perpendicular to its surface. The longest wavelength in nm which is constructively reflected, assuming soap has the same index of refraction as water (n = 1.33) is equal to 505.4 nm. Draw a diagram of the mediums showing where, if any, a phase change occurs. State whether you are looking for constructive of destructive interference.
Light with wavelength 530 nm in air (n = 1) passes through a soap bubble (n...
Light with wavelength 530 nm in air (n = 1) passes through a soap bubble (n = 1.33), where its wavelength becomes ≈ 400 nm. A What is the phase difference between a light wave reflected off the surface of the bubble and one that passes into it before being reflected? B The thickness of the bubble is 100 nm. Does this lead to constructive or destructive interference? C What would happen for a soap film covering a glass surface...
A spectrum of visible light colors from 400 nm to 700 nm is incident on a...
A spectrum of visible light colors from 400 nm to 700 nm is incident on a diffraction grating that has 500 lines per mm, projecting a pattern on a screen 2.4 m behind the grating. a. Determine the width of the spectrum that corresponds to m = 1 b. How much distance separates the end of the m = 1 spectrum and the start of the m = 2 spectrum?
A soap film (n=1.33) is 772 nm thick. White light strikes the film at normal incidence....
A soap film (n=1.33) is 772 nm thick. White light strikes the film at normal incidence. What visible wavelengths will be constructively reflected if the film is surrounded by air on both sides? If there is more than one answer, separate them by a comma.
5. Find all the wavelengths of visible light emitted when Hydrogen is heated. Approximate visible light...
5. Find all the wavelengths of visible light emitted when Hydrogen is heated. Approximate visible light to have the range from 400 nm to 700 nm. No points for only telling the wavelengths. Points will be for showing how you found these wavelengths (mention the transitions).
A narrow beam of light containing red (660 nm) and yellow (580 nm) wavelengths goes from...
A narrow beam of light containing red (660 nm) and yellow (580 nm) wavelengths goes from polystyrene to air, striking the surface at a 34.5° incident angle. What is the angle (in degrees) between the colors when they emerge? ° (b) How far would they have to travel (in m) to be separated by 1.00 mm? m
A beam of light containing red (660 nm) and violet (410 nm) wavelengths travels from air,...
A beam of light containing red (660 nm) and violet (410 nm) wavelengths travels from air, through a flat piece of crown glass 1.92 cm thick, and then back to air. (a) If the beam has an angle of incidence of 36.0° in air, determine the angle at which the two colors of light emerge from the crown glass. The index of refraction respectively for red and violet light in crown glass is 1.512 and 1.530. (Enter a number to...
A physics instructor wants to project a spectrum of visible-light colors from 400 nm to 700...
A physics instructor wants to project a spectrum of visible-light colors from 400 nm to 700 nm as part of a classroom demonstration. She shines a beam of white light through a diffraction grating that has 600 lines per mm, projecting a pattern on a screen 2.9 m behind the grating. How wide is the spectrum that corresponds to m = 1? Express your answer with the appropriate units. How much distance separates the end of the m = 1...
While the human eye responds to light with wavelengths up to about 750 nm, it is...
While the human eye responds to light with wavelengths up to about 750 nm, it is hard to distinguish the color of different wavelengths between 650 and 700 nm. Why?
The human eye can readily detect wavelengths from about 400 nm to 700 nm
The human eye can readily detect wavelengths from about 400 nm to 700 nm.If white light illuminates a diffraction grating having 730 lines/mm, over what range of angles does the visible m = 1 spectrum extend? Express your answers using three significant figures separated by a comma.θmin, θmax= ____________degrees
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT