Respuesta :
A film of soapy water (n = 1. 33) on top of a plastic cutting board (n > 1. 33) has a thickness of 147 nm. The color that is most strongly reflected if it is illuminated perpendicular to its surface is 294nm.
When the light is reflected it experiences a half of phase change. Then, the ray will be refracted by travelling through the soapy water down due to the refractive index. It will hit the second boundary which is plastic but light does not pass through the plastic. This will again reflect with again half of a phase change.
So, the formula used is:
2t = λ / 2 + λ / 2
Given,
refractive index of soap = 1.33
refractive index of air = 1
The relation between the thickness of the board and the wavelength used is as follows:
2t = λ / 2 + λ / 2
where, t is the thickness
λ is wavelength
On solving,
2t = λ
On substituting in above equation,
2(147) = λ
λ = 294nm
The color that is most strongly reflected if it is illuminated perpendicular to its surface is 294nm.
Learn more about refractive index here, https://brainly.com/question/23750645
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