What is the minimum thickness of a soap film that appears dark when illuminated by white light?

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Q: What is the minimum thickness of a soap film that appears dark when illuminated by white light?

Solution: For destructive interference in a soap film, the minimum thickness should be λ/2, considering the phase change upon reflection.

Steps: 6

Step 1: Understand that a soap film can create colors due to interference of light.
Step 2: Know that when light hits the soap film, some light reflects off the top surface and some goes through to reflect off the bottom surface.
Step 3: Recognize that for destructive interference (which makes the film appear dark), the light waves need to cancel each other out.
Step 4: Remember that when light reflects off a medium with a higher index of refraction (like soap), it undergoes a phase change of 180 degrees (or half a wavelength).
Step 5: For the minimum thickness of the soap film to appear dark, the path difference between the two reflected light waves must be equal to half a wavelength (λ/2).
Step 6: Therefore, the minimum thickness of the soap film that appears dark is λ/2.