Question

A soap bubble has a thickness of 100 nm and a refractive Index of 1.35. Given that the wavelength of red light is about 700 nm and that of blue light is 400 nm, what colour does the bubble appear to be at the point on its surface closest to an observer when it is illuminated by white light?

A
White
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B
Black
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C
Red
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D
Green
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Solution

The correct option is D GreenGiven: A soap bubble has a thickness of 100 nm and a refractive Index of 1.35. Given that the wavelength of red light is about 700 nm and that of blue light is 400 nm, To find what colour does the bubble appear to be at the point on its surface closest to an observer when it is illuminated by white lightSolution:The light will be transmitted through the soap bubble occurs for same condition as for minimum reflection and the transmitted light will be in phase with the incident light (phase is never inverted on transmission). The light reflected from the internal surface will also be in phase with the incident light. the film thickness must be λ4.And as per the given criteria,μfilm=1.35,tfilm=100nmWe know, λfilm=4t⟹λfilm=2×100nm⟹λfilm=400nmnow,μfilm=λairλfilm⟹λair=1.35×400nm⟹λair=540nmLight with wavelength 540nm will be transmitted through and it is the wavelength of green color. The soap film will, therefore, possess a pronounced green colour.

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