What is the minimum thickness of a soap bubble that appears black in reflected light?

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Q: What is the minimum thickness of a soap bubble that appears black in reflected light?

Solution: A soap bubble appears black in reflected light when the thickness is λ/4, leading to destructive interference.

Steps: 8

Step 1: Understand that a soap bubble has two surfaces: the outer surface and the inner surface.
Step 2: When light hits the bubble, some light reflects off the outer surface and some light reflects off the inner surface.
Step 3: The light reflecting off the inner surface travels a little further than the light reflecting off the outer surface.
Step 4: For the bubble to appear black, the two reflected light waves must cancel each other out. This is called destructive interference.
Step 5: Destructive interference occurs when the difference in the path lengths of the two light waves is equal to half a wavelength (λ/2) or an odd multiple of it.
Step 6: However, because of a phase change that occurs when light reflects off a denser medium (like the soap), we need to adjust our condition for destructive interference.
Step 7: This adjustment means that for the bubble to appear black, the effective thickness of the bubble must be λ/4, where λ is the wavelength of the light.
Step 8: Therefore, the minimum thickness of the soap bubble that appears black in reflected light is λ/4.