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

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Q: What is the minimum thickness of a soap bubble that will appear 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 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: This extra distance can cause the two reflected light waves to interfere with each other.
Step 5: For the bubble to appear black, the two waves must cancel each other out, which is called destructive interference.
Step 6: Destructive interference occurs when the difference in distance traveled by the two waves is equal to half a wavelength (λ/2) or an odd multiple of it.
Step 7: However, because one wave reflects off a denser medium (the soap), it undergoes a phase change of π (or half a wavelength).
Step 8: To achieve destructive interference, the effective path difference must be λ/4, which is the condition for the bubble to appear black.