Question

A film of soapy water (n=1.33) on top of a plastic cutting board has a thickness of 233 nm. What color is most strongly reflected if it is illuminated perpendicular to its surface?

Answer 1

The most strongly reflected color is red light, which has a wavelength of approximately 660 nm.

Step-by-step explanation:

When light passes through a film of soapy water, it undergoes interference due to the difference in thickness of the film. The most strongly reflected color is the one that experiences constructive interference. Constructive interference occurs when the path difference between the reflected waves is an integer multiple of the wavelength. In this case, for the film of soapy water with a thickness of 233 nm, we can use the equation for constructive interference in a film:

2nt = mλ

Where 'n' is the refractive index of the film, 't' is the thickness of the film, 'm' is the order of interference, and 'λ' is the wavelength of the reflected light. Since the film is illuminated perpendicular to its surface, the order of interference 'm' is 1. By substituting the given values, we can solve for the wavelength of the reflected light:

2(1.33)(233 nm) = (1)(λ)

λ ≈ 660 nm

The most strongly reflected color is red light, which has a wavelength of approximately 660 nm.