Final answer:
The colors seen in a soap bubble are a result of thin film interference, which enhances specific wavelengths of light. For a soap bubble with an index of refraction of 1.36 and a thickness of 380 nm, the wavelength of the reflected light that appears enhanced is approximately 380 nm.
Step-by-step explanation:
When light waves strike a soap bubble, they undergo a phenomenon called thin film interference. This interference causes some wavelengths of light to be enhanced, resulting in the appearance of certain colors.
The colors seen in a soap bubble depend on the thickness of the bubble and the index of refraction of the soap film.
For a soap bubble with an index of refraction of 1.36 and a thickness of 380 nm, the wavelengths of light that are most constructively reflected are those that experience a phase change of 180 degrees upon reflection.
These wavelengths can be calculated using the formula:
2t = (m + 0.5) * λ / n
Where:
- t is the thickness of the soap bubble
- m is an integer representing the order of the interference
- λ is the wavelength of the incident light
- n is the index of refraction of the soap film
In this case, since we are looking for the most constructively reflected light, we can assume m = 0. By rearranging the formula, we can solve for the wavelength of the reflected light:
λ = (2t * n) / (m + 0.5)
Substituting the given values, we find that the wavelength of the reflected light that appears enhanced in the soap bubble is approximately 380 nm.