How Does Soap Bubble Thickness Affect Color Wavelength Interference?

[stickplot]

Homework Statement

Ok I have two questions.
1. 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

2. You are outside in the Sun blowing bubbles. As you raise the round wand to blow bubbles, you notice an array of colors on the soap film.
Blue = 430 nanometers
Green = 500 nanometers
Red = 650 nanometers
The bubble film has an index of refraction of n = 1.3.

a. How thick is the film where you see yellow?

b. How thick is the film where you see cyan?

Homework Equations

1. 1/2 of a wavelength is destructive.
2. There are many equations but i don't know which one is right for the problem I am not sure how to find the thickness.

The Attempt at a Solution

1. A will destructively interfere with the bubble film
1/2x430= 215
215/1.3= 165
(my answer not 100% sure but I am pretty sure just need confirmation)


2. yellows wavelength is 570 nm
cyans is 470 nm
I am not sure what to do to find the thickness. can someone help please.


Thank you

 

[anathema]

for your questions. Let's start with the first one.

1. To determine which wavelength will destructively interfere with the bubble film, we can use the equation for destructive interference: 1/2λ = t (where λ is the wavelength and t is the thickness of the film). We know that t = 165 nm and n = 1.3. Plugging these values into the equation, we get:

1/2λ = 165 nm x 1.3
λ = 215.5 nm

Therefore, the wavelength that will destructively interfere with the bubble film is 215.5 nm. Since this is the closest to option a (430 nm), your answer is correct.

2. To find the thickness of the film where you see yellow and cyan, we can again use the equation for destructive interference. We know that yellow has a wavelength of 570 nm and cyan has a wavelength of 470 nm. Plugging these values into the equation, we get:

1/2λ = t (where t is the thickness of the film)

For yellow:
1/2(570 nm) = t
t = 285 nm

For cyan:
1/2(470 nm) = t
t = 235 nm

Therefore, the thickness of the film where you see yellow is 285 nm and the thickness of the film where you see cyan is 235 nm.

 

[nlightner]

for your questions. Let me address them one by one.

1. To find the wavelength that will destructively interfere with the bubble film, we need to use the equation for destructive interference: d = (m + 1/2)λ/n, where d is the thickness of the film, m is the number of times the light wave reflects off the top and bottom of the film, λ is the wavelength of the light, and n is the index of refraction of the film. We can rearrange this equation to solve for λ, which gives us λ = (d - (m + 1/2))n. Plugging in the given values, we get:

λ = (165 nm - (0 + 1/2)) x 1.3 = 165 nm - 0.65 nm = 164.35 nm

This means that a light wave with a wavelength of 164.35 nm will destructively interfere with the bubble film.

2. To find the thickness of the film where you see yellow and cyan, we can use the same equation as above, but this time we will solve for d. Since we know the wavelengths of yellow and cyan light, we can plug those in and solve for d.

a. For yellow light (λ = 570 nm), we get:

d = (0 + 1/2) x 570 nm / 1.3 = 285 nm / 1.3 = 219.23 nm

Therefore, the thickness of the film where you see yellow is approximately 219.23 nm.

b. For cyan light (λ = 470 nm), we get:

d = (0 + 1/2) x 470 nm / 1.3 = 235 nm / 1.3 = 180.77 nm

Therefore, the thickness of the film where you see cyan is approximately 180.77 nm.

I hope this helps! Let me know if you have any further questions.