Final answer:
The subject is thin film interference in physics, where the wavelength and color of visible light most constructively reflected by a 100 nm thick soap bubble are sought. While the first order of constructive interference yields a wavelength in the ultraviolet range, the visible color seen would be due to a higher-order interference, and without precise calculations for these higher orders, the exact color cannot be determined.
Step-by-step explanation:
The subject of this question is thin film interference, a concept in physics that explains how different wavelengths of light can constructively or destructively interfere with each other when they reflect from different layers of a thin film. In the case of a soap bubble that is 100 nm thick and illuminated by white light at a 45° angle, we have to find the wavelength and color of visible light that is most constructively reflected, assuming the same index of refraction as water, which is approximately 1.33.
To find the wavelength of the light that is most constructively reflected, we use the formula for constructive interference in thin films:
2 * t * n = m * λ
where t is the thickness of the film, n is the index of refraction of the film, m is an integer representing the order of the interference, and λ is the wavelength of light. For the first order of interference (m=1) and a given thickness and index of refraction, we can solve for λ. Once we have the wavelength, we can relate it to the corresponding color visible to the human eye.
Since the index of refraction for water is taken to be around 1.33 and the bubble is 100 nm thick, for the first order of constructive interference (m = 1), the wavelength (λ) of light that is most constructively reflected would match this thickness. We must also take into account the angle of incidence by using Snell's law to correct the effective path difference and thickness. However, as the question asks to ignore angle effects, we simplified the calculation as:
2 * 100 nm * 1.33 = 1 * λ
Hence, λ = 266 nm, which is in the ultraviolet range. However, since we are asked about the visible spectrum, we would instead look for a higher order (higher m value) where λ falls into the visible range (approximately 380 nm to 750 nm). The most constructive reflection in the visible spectrum would be a higher order of interference.
The colors in the visible spectrum range from violet (400 nm) to red (700 nm). Without the exact mathematical work for higher order reflections, we cannot specify which exact color from the visible spectrum will be most strongly reflected.