What is the Explanation for the Interference Pattern in Thin Soap Films?

[EmilyBergendahl]

Homework Statement

Green light is shone onto two soap films. An observer looking down at the soap films sees that soap film X appears uniformly green while soap film Y has green and black bands. If air is the medium on either side of the soap film, the best explanation of this pattern is that:

A) film X has a thickness much less than λ and film Y has a thickness of 1/4 λ
B) film X has a thickness of 1/2 λ and film Y has a thickness of 1/4 λ
C) film X has a thickness of 1/4 λ and film Y has a thickness of 1/2 λ
D) film X has consistent thickness throughout whereas film Y has variable thickness
E) film X has variable thickness whereas film Y has consistent thickness throughout

Homework Equations

None given

The Attempt at a Solution

Because film X appears uniformly green, we know that it is of a consistent thickness. Therefore, the answer is not (E). The answer is also not (C), because it would cancel due to destructive interference.

I'm leaning towards either (B) or (D), but I would like clarification on (A)... I don't understand what "much less than λ" means in the context of the question.

 

[ehild]

Homework Statement

Green light is shone onto two soap films. An observer looking down at the soap films sees that soap film X appears uniformly green while soap film Y has green and black bands. If air is the medium on either side of the soap film, the best explanation of this pattern is that:

A) film X has a thickness much less than λ and film Y has a thickness of 1/4 λ
B) film X has a thickness of 1/2 λ and film Y has a thickness of 1/4 λ
C) film X has a thickness of 1/4 λ and film Y has a thickness of 1/2 λ
D) film X has consistent thickness throughout whereas film Y has variable thickness
E) film X has variable thickness whereas film Y has consistent thickness throughout

Homework Equations

None given

The Attempt at a Solution

Because film X appears uniformly green, we know that it is of a consistent thickness. Therefore, the answer is not (E). The answer is also not (C), because it would cancel due to destructive interference.

I'm leaning towards either (B) or (D), but I would like clarification on (A)... I don't understand what "much less than λ" means in the context of the question.

It is the phase difference between the directly reflected light wave and the one reflected from the back surface of the film, that determines if the interference is constructive or destructive. The phase can change π or zero at the interfaces and it changes by (4π/λ)d inside the film, where λ is the wavelength in the film material, and d is the film thickness. If d << λ this phase change is negligible and the interference is determined by the phase changes at the boundaries.

 

[Simon Bridge]

You can decide between A, B, and D by thinking about how colored and black bands form.

 

[EmilyBergendahl]

Okay. Thank you both for your responses!

It is the phase difference between the directly reflected light wave and the one reflected from the back surface of the film, that determines if the interference is constructive or destructive. The phase can change π or zero at the interfaces and it changes by (4π/λ)d inside the film, where λ is the wavelength in the film material, and d is the film thickness. If d << λ this phase change is negligible and the interference is determined by the phase changes at the boundaries.

I'm still a bit confused about the wording in the problem's answer. If, for example, "much less than λ" was ½λ in this case, wouldn't (A) then produce the same result as (B)?

You can decide between A, B, and D by thinking about how colored and black bands form.

The bright bands are formed by constructive interference between the light rays reflected from both surfaces, while the dark bands are caused by destructive interference. So, if I graph the waves, (B) interferes constructively and (C) interferes destructively. But wouldn't you need both types of interference to see the bands on the film? I'm having trouble relating my thought process to the solutions presented in the problem.

I'm sorry if I seem a bit slow with this... I missed the entire unit at school due to illness, and now I'm trying to teach myself while reviewing for the exam (not a ideal combination by any means). Any clarification at all is greatly appreciated!

 

[ehild]

Okay. Thank you both for your responses!
I'm still a bit confused about the wording in the problem's answer. If, for example, "much less than λ" was ½λ in this case, wouldn't (A) then produce the same result as (B)?

½λ is not much less than λ. It is better to consider the thickness about zero.

 

[EmilyBergendahl]

½λ is not much less than λ. It is better to consider the thickness about zero.

Okay. So upon graphing the examples again with (A) at nearly zero, it seems that (A) and (B) form almost identical graphs... Should this be happening? I feel like I'm still doing something wrong.

 

[ehild]

The phase of the incident wave changes by pi upon reflection, while the wave entering into the film has no phase change when reflected from the film-air interface. If the film is very thin, the phase change due to the thickness can be ignored, so the phase difference between the reflected waves is pi. is it constructive or destructive interference?

 

[EmilyBergendahl]

I think that it is constructive interference.

 

[ehild]

Okay. So upon graphing the examples again with (A) at nearly zero, it seems that (A) and (B) form almost identical graphs... Should this be happening? I feel like I'm still doing something wrong.

Your graph does not correspond to the situation. You have a film with air on both sides, and not an air layer between glass plates.
When do you get dark and bright bands on the film? Is it possible with a film of homogeneous thickness?

 

[ehild]

I think that it is constructive interference.

Why? If the phase difference is pi between two sine function, one has maximum when the other one has minimum, what do you get if adding them?

 

[EmilyBergendahl]

Oh, yes, you're right... It should be destructive because they would add to zero/cancel out.

You cannot get bands with a film of homogeneous thickness. We know that Film X is of a consistent thickness because it appears uniformly green to the viewer.

Therefore, if I'm not misunderstanding this, the answer should be (D), because the bands must be produced by a film of inconsistent thickness.

 

[ehild]

Oh, yes, you're right... It should be destructive because they would add to zero/cancel out.

You cannot get bands with a film of homogeneous thickness. We know that Film X is of a consistent thickness because it appears uniformly green to the viewer.

Therefore, if I'm not misunderstanding this, the answer should be (D), because the bands must be produced by a film of inconsistent thickness.

Yes, D is true.

 

[EmilyBergendahl]

Great! Thank you for all your help ehild! I feel like I better understand the concepts related to this question now.