A soap bubble has an index of refraction of 1.33.What minimum thickness of this bubble will ensure maximum reflectance of normally-incident light having a wavelength of 530 nm?
A)24.9 nm
B)76.9 nm
C)99.6 nm
D)199 nm
E)398 nm

Question

Quizplus · Accepted Answer

For maximum reflectance in thin films under normal incidence, the path difference should be an odd multiple of half wavelengths in the medium. The minimum thickness for maximum reflectance occurs when this path difference is equal to half the wavelength in the medium. The effective wavelength in the medium ($\lambda'$) is the wavelength in vacuum ($\lambda$) divided by the index of refraction ($n$), so $\lambda' = \lambda / n$. For a soap bubble, the light travels through the film and reflects off the back surface, effectively doubling the path length the light travels through the film. Therefore, the condition for the first maximum (minimum thickness) is $2t = \lambda' / 2$, where $t$ is the thickness of the film. Rearranging for $t$, we get $t = \lambda' / 4 = (\lambda / n) / 4$. Substituting $\lambda = 530$ nm and $n = 1.33$, we find $t = (530 \, \text{nm} / 1.33) / 4$, which calculates to approximately 99.6 nm.

A Soap Bubble Has an Index of Refraction of 1