A small boy blows a big soap bullet at a birthday party where the room is illuminated with yellow light of wavelength 600 nm.
a) What is the colour of the soap bubble? Give reasons for your answer.
b) Estimate the thickness of the soap bubble. [Refractive index of soap bubble solution= 1.40]
c) If the room is illuminated with sunlight, explain briefly what will happen to the appearance of the soap bubble?
a) To determine the color of the soap bubble, we need to understand the phenomenon of interference. When light passes through and reflects off the thin film of a soap bubble, interference occurs between the reflected light waves. This interference causes certain wavelengths to cancel each other out while reinforcing others, resulting in different colors being observed.
Soap bubbles typically appear colorful due to the phenomenon of thin-film interference. The thickness of the soap bubble determines the color observed. In this case, the room is illuminated with yellow light of wavelength 600 nm. Yellow light has a relatively longer wavelength compared to other colors in the visible spectrum. When this yellow light interacts with the thin film of the soap bubble, it undergoes constructive and destructive interference.
Constructive interference occurs when the path length difference of the reflected waves is a multiple of the wavelength. In this case, the yellow light with a wavelength of 600 nm will have constructive interference within a certain range of soap bubble thickness. Therefore, we can expect to observe a yellow color in the soap bubble.
b) To estimate the thickness of the soap bubble, we can use the formula for the thickness of a thin film:
Thickness = (wavelength in vacuum) / (2 * refractive index * number of interference maxima)
In this case, the wavelength is 600 nm (0.6 μm), and the refractive index of the soap bubble solution is given as 1.40. We need the number of interference maxima, which corresponds to the number of bright color bands observed in the soap bubble.
To estimate the number of interference maxima, we need to consider the fact that a soap bubble is approximately an optical path of two times its thickness. For constructive interference of light with itself, we use the equation:
Path Length Difference = m * λ
Where m is the order of the maxima, λ is the wavelength, and the path length difference is 2 * thickness.
By rearranging the equation:
m = (2 * thickness) / λ
Since we expect to observe at least one color band, we can assume m = 1. Substituting the known values:
1 = (2 * thickness) / 0.6 μm
Simplifying the equation:
2 * thickness = 0.6 μm
thickness = (0.6 μm) / 2
Therefore, the estimated thickness of the soap bubble is 0.3 μm.
c) If the room is illuminated with sunlight, the appearance of the soap bubble can change. Sunlight is a white light source, which consists of a broad range of wavelengths across the visible spectrum.
When sunlight illuminates the soap bubble, the different wavelengths of light will undergo constructive and destructive interference, resulting in a display of multiple colors. This effect is known as iridescence.
The colors observed in the soap bubble under sunlight will depend on the thickness of the bubble and the interference pattern created by different wavelengths. As the thickness of the bubble varies across its surface, different parts of the bubble will exhibit different colors. This can create beautiful, shimmering effects as the soap bubble moves or changes shape.
In summary, when the room is illuminated with sunlight, the appearance of the soap bubble will change due to the broad spectrum of light causing interference and creating a multitude of colors.