Q: The soap film comprising a bubble is 102 nm thick and has refractive index 1.33. What visible wavelength is best reflected from this bubble? Assume air on both sides and normal viewing angle.
🌈 Step 1: Understand the Scenario
A soap film surrounded by air on both sides causes interference of light reflected from its surfaces. Light reflects off both the top and bottom surfaces, producing a visible interference pattern.
- Top Surface (Air → Film): Higher refractive index causes a π phase shift.
- Bottom Surface (Film → Air): Lower refractive index causes no phase shift.
Thus, there is a net phase shift of π (half-wavelength) that must be accounted for in interference conditions.
🔍 Step 2: Condition for Constructive Interference
The extra path traveled by the wave inside the film is twice the thickness:
Extra Optical Path = 2 × n × t
The condition for constructive interference with one phase reversal (π) is:
2nt = (m + 0.5)λ → For smallest m = 0: λ = 4nt
✏️ Step 3: Plug in Values
Given:
- n = 1.33
- t = 102 nm
λ = 4 × 1.33 × 102 = 543.36 nm
This wavelength falls within the green portion of the visible spectrum.
✅ Final Answer
The visible wavelength that is best reflected from the soap bubble is approximately:
λ ≈ 543 nm
This corresponds to the green color in the visible spectrum.