A soap bubble with walls 401 nm thick floats in air. If this bubble is illuminated with sunligh

step 1 Here in this question we have given thickness equals to 401 nanometer which can be written as 40

A soap bubble with walls 401 nm thick floats in air. If...

A soap bubble with walls $401 \mathrm{~nm}$ thick floats in air. If this bubble is illuminated with sunlight (wavelengths from $400 \mathrm{~nm}$ to $700 \mathrm{~nm}$ ), what wavelength will be absent in the reflected light? Assume that the index of refraction of the soap film is $1.33$.

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Key Concepts

Thin Film Interference

This concept involves the interference of light waves reflecting off the two surfaces of a thin film. The waves can interfere constructively or destructively depending on their phase difference, which leads to selective enhancement or cancellation of specific wavelengths and produces the colorful patterns often seen in thin films.

Optical Path Difference

This is the effective difference in the distance that light travels in a medium compared to air, taking into account the refractive index. In thin film interference, the optical path difference between the two reflected waves determines their relative phase and therefore whether they reinforce or cancel each other.

Phase Shift upon Reflection

When light reflects at an interface between two media of differing refractive indices, a phase shift can occur. Specifically, a reflection from a medium of lower index to a higher index introduces a half-wavelength (? radians) phase shift. This phase difference is crucial in setting the precise conditions for constructive or destructive interference in thin films.

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