Final answer:
The thickness of a soap bubble's wall is key to thin film interference, leading to the appearance of various colors. For a bubble to appear red at a wavelength of 680 nm, its thickness is roughly 170 nm, which places the thickness within the 400-800 nm range of visible light wavelengths.
Step-by-step explanation:
The color of a soap bubble can be explained by thin film interference, a phenomenon that occurs when light waves reflected from the top and bottom surfaces of the bubble interfere with one another. The constructive interference of these waves can cause certain colors to be reflected more strongly, which depends on the thickness of the film and the wavelength of light. For visible light, with wavelengths ranging from 400 to 800 nm, the thickness of the soap bubble's wall is comparable to these wavelengths, causing interference patterns that result in iridescent colors.
When a double-surface soap bubble is illuminated by white light, we typically see bright colors due to constructive interference when the path length difference is a multiple of the wavelength. The bubble appears red (at around 680 nm wavelength) when its thickness leads to constructive interference at that wavelength of light. The approximate thickness for a red appearance, considering the reflected wave suffers a 180-degree phase shift at the air-film interface, is around 680 nm/4 or 170 nm.
Therefore, the answer to the student's question is that the thickness is between 400 and 800 nm, which is option c. This range allows for the interference patterns that give the bubbles their characteristic colors.