Destructive Interference of Light in 165nm Bubble Film

[stickplot]

Homework Statement

Light waves of which wavelength will destructively interfere due to the thickness of the bubble film? The bubble film thickness is 165 nm, with an index of refraction of n = 1.3.

a= 430 nm
b= 650 nm
c= 860 nm
d= 285 nm
(different wavelengths)

Homework Equations

The Attempt at a Solution

for the interference to be destructive the wave passing through the bubble thickness is delayed by half a wavelength. The wavelength of the light decreases when it passes into the bubble film.
I know this but i just don't know how to apply it to a equation and the problem

 

[Carid]

The half wavelength path difference corresponds to a light ray traversing the bubble film and being reflected from the inner bubble surface. So the path difference is twice the bubble thickness modulated by the effect of the refractive index. How does the refractive index alter the effective path length? Well you can try either multiplying or dividing by the given value of 1.3 to get the right mathematical result by comparison with the multiple choices; more important is to try to understand physically why light behaves like this in a transparent medium.

 

[nlightner]

.

I would approach this problem by first understanding the concept of destructive interference. This occurs when two waves with the same frequency and amplitude are out of phase with each other, resulting in a cancellation of the wave amplitudes. In order for this to occur, the path difference between the two waves must be equal to an integer multiple of half the wavelength.

In this case, we are given the thickness of the bubble film (165 nm) and the index of refraction (1.3). We can use the equation nλ = d (where n is the index of refraction, λ is the wavelength, and d is the thickness of the film) to determine the wavelength of the light passing through the bubble film.

Substituting in the values, we can solve for the wavelength:

1.3λ = 165 nm

λ = 165 nm / 1.3

λ = 127 nm

This means that the wavelength of light passing through the bubble film is 127 nm. Now, we can compare this to the given wavelengths (a= 430 nm, b= 650 nm, c= 860 nm, d= 285 nm) to determine which will result in destructive interference.

Since the wavelength passing through the bubble film is significantly smaller than the given wavelengths, it is likely that all of these wavelengths will result in destructive interference. However, we cannot determine exactly which ones will without knowing the phase difference between the waves.

In conclusion, the destructive interference of light in a 165 nm bubble film will depend on the phase difference between the waves, but it is likely that all of the given wavelengths will result in destructive interference.