(I) If a soap bubble is 120 nm thick, what wavelength is most strongly reflected at the center of the outer surface when illuminated normally by white light? Assume that n = 1.35.

Verified step by step guidance

1. Identify the given values: thickness of the soap bubble (t = 120 nm) and the refractive index of the soap bubble (n = 1.35).
2. Understand that the phenomenon described is thin-film interference, which occurs due to the constructive interference of light waves reflecting off the front and back surfaces of the thin film.
3. Use the formula for constructive interference in thin films: \(2nt = m\lambda\), where \(m\) is the order of the interference (typically the first order, m=1, is considered for maximum reflection), \(n\) is the refractive index, \(t\) is the thickness of the film, and \(\lambda\) is the wavelength of light.
4. Solve for \(\lambda\) using the equation \(\lambda = \frac{2nt}{m}\). Plug in the values: \(n = 1.35\), \(t = 120 \text{ nm}\), and \(m = 1\).
5. Calculate the wavelength \(\lambda\) that corresponds to the first order of maximum constructive interference, which will be the wavelength most strongly reflected.

Key Concepts

Thin Film Interference

Thin film interference occurs when light waves reflect off the two surfaces of a thin film, such as a soap bubble. The reflected waves can interfere constructively or destructively depending on the film's thickness and the wavelength of light. This phenomenon is responsible for the colorful patterns seen in soap bubbles.

Wavelength and Refractive Index

The refractive index (n) of a material affects how light travels through it, altering the effective wavelength of light within the medium. For a soap bubble with a refractive index of 1.35, the wavelength of light in the film is shorter than in a vacuum. This change is crucial for determining which wavelengths are most strongly reflected.

Constructive Interference Condition

Constructive interference occurs when the path difference between two reflected light waves is an integer multiple of the wavelength. For a soap bubble, the condition for constructive interference is given by 2nt = mλ, where n is the refractive index, t is the thickness of the film, m is an integer, and λ is the wavelength in a vacuum. This relationship helps identify the wavelengths that will be most prominently reflected.