A 500-nm-wavelength beam of light illuminates a soap film with air on both sides and an index of refraction 1.33.If the beam of light is incident normally on the film,what is the minimum thickness of the film to make the reflected light enhanced in brightness?

Question

Quizplus · Accepted Answer

When a beam of light of wavelength 'λ' is normally incident on a soap film of thickness 't', the reflected light waves from the two interfaces of the film interfere. 
If the reflected waves from both interfaces are in phase, they reinforce each other and produce constructive interference resulting in enhanced brightness.
For constructive interference,
2t = (m + ½)λ/n
where 'm' is the order of the interference, 'n' is the refractive index of the film, and λ is the wavelength of the incident light.
For the given problem, 
λ = 500 nm (given), n = 1.33 (given), and since we want the minimum thickness for constructive interference, we take m = 0.
Thus we have,
2t = λ/n
=> 2t = (500 nm)/(1.33)
=> t = (500/2) nm / 1.33
=> t = 187.97 nm
Since the soap film has air on both sides, the minimum thickness required for constructive interference is half of 187.97 nm.
Minimum thickness, t = 94.0 nm
Therefore, the correct answer is C) 94.0 nm.

A 500-Nm-Wavelength Beam of Light Illuminates a Soap Film with Air