Path diffrence to produce destructive intefrence

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In summary: So the ans is (n-1) t = (m-0.5) λ. I'm sorry, it's my mistake. I'll try to be more careful in the future. In summary, the condition for destructive interference to occur at a point D, where there is a dark band, when a transparent film of thickness t and reflective index n is placed in front of Y is (n-1) t = m λ, where m is the number of dark bands and λ is the wavelength. This is because the total path difference for destructive interference should be (m-0.5)λ, and the path difference for the film
  • #1
somecelxis
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Homework Statement



A transparent flim of thickness t and reflective index n is placed in front of Y . Which one shows the new condition for destructive intefrence to occur ? the ans is (n-1) t = m λ
. In my opinion , it should be (n-1) t = (m-0.5) λ ,
because for destructive interference to occur , the path difference should be 0.5λ

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  • #2
You seem to be pretty lazy (which may be a good quality) not filling in 2 and 3. Never mind. Could you be so good as to post the problem statement in facsimile too ? Is it a multiple choice thing (since it asks "Which one shows.."). And how do you know the ans ?
 
  • #3
Code:
somecelxis said:
A transparent flim of thickness t and reflective index n is placed in front of Y . Which one shows the new condition for destructive intefrence to occur ? the ans is (n-1) t = m λ
. In my opinion , it should be (n-1) t = (m-0.5) λ ,
because for destructive interference to occur , the path difference should be 0.5λ
From what you've written, I surmise that the question may actually be along these lines...

There is a point (which I'll denote as D) where there is a dark band. The piece of film is placed in front of Y. What is the condition for destructive interference to again occur at that point D?
 
  • #4
NascentOxygen said:
Code:
From what you've written, I surmise that the question may actually be along these lines...

There is a point (which I'll denote as D) where there is a dark band. The piece of film is placed in front of Y. What is the condition for destructive interference to again occur at that point D?

yes , this is roughly what the question means .
 
  • #5
NascentOxygen said:
Code:
From what you've written, I surmise that the question may actually be along these lines...

There is a point (which I'll denote as D) where there is a dark band. The piece of film is placed in front of Y. What is the condition for destructive interference to again occur at that point D?

In my opinion , it should be (n-1) t = (m-0.5) λ
Am i correct?
for destructive interfrence to occur , the phase difference must be (m-0.5)λ.
i.e. destructive interfrence occur at 0.5λ (180 °) , 1.5λ (540°) ...
 
  • #6
Could you be so good as to post the problem statement in facsimile too ? Is it a multiple choice thing (since it asks "Which one shows.."). And how do you know the ans ?

for destructive interfrence to occur , the phase difference must be (m-0.5)λ
I think we can agree on that :smile:
 
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  • #7
somecelxis said:
In my opinion , it should be (n-1) t = (m-0.5) λ
Am i correct?
No.
for destructive interfrence to occur , the phase difference must be (m-0.5)λ.
i.e. destructive interfrence occur at 0.5λ (180 °) , 1.5λ (540°) ...
The total phase difference must be (m-0.5)λ, yes.
 
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  • #8
NascentOxygen said:
No.

The total phase difference must be (m-0.5)λ, yes.

since you said my (m-0.5)λ, is correct... then why my (n-1) t = (m-0.5) λ is wrong?
 
  • #9
the other options are nt= mλ, (n-1) t = m λ , (n+1) t = m λ , and (n+1)t = 0.5mλ...
my choice is (n+1)t = 0.5mλ ... Am i wrong ?
 
  • #10
NascentOxygen said:
No.

The total phase difference must be (m-0.5)λ, yes.

the other options are nt= mλ, (n-1) t = m λ , (n+1) t = m λ , and (n+1)t = 0.5mλ...
my choice is (n+1)t = 0.5mλ ... Am i wrong ?
 
  • #11
There is not much point just guessing. It's time to draw some diagrams and think about this really closely.

Attach your diagrams so we can see how you go about it.
 
  • #12
well celxis, O2 has me puzzled too. I don't think there's a phase jump involved, and I also think the path difference is (n-1)t (didn't mean to create the impression that it isn't, in post #6), so his (her?) no in post #7 must have some other reason. something about m that we all take for granted ?

By the way, does the film have a reflective index n or an index of refraction n ?

And I do hope your + in the last line of post 10 was a typo. Stick to the minus sign...
 
  • #13
SORRY ， all。 please ignore my few post before it. my ans is still (n-1) t = (m-0.5) λ , but the ans is (n-1) t = m λ..
there 're few choices :
nt= mλ, (n-1) t = m λ , (n+1) t = m λ , and (n+1)t = 0.5mλ..

reason for my choice :
because for destructive interference to occur , the path difference should be 0.5λ
 

FAQ: Path diffrence to produce destructive intefrence

1. What is path difference in the context of destructive interference?

Path difference refers to the difference in distance traveled by two waves from their sources to a specific point where they overlap. In the context of destructive interference, this difference in path length causes the waves to be out of phase and cancel each other out, resulting in a decrease in intensity or amplitude at that point.

2. How is path difference calculated?

Path difference can be calculated by finding the difference in the distances traveled by the two waves from their sources to a specific point. This can be done by measuring the distance between the sources and the point of overlap, or by using the wavelength and angle of incidence of the waves.

3. What is the relationship between path difference and wavelength?

The relationship between path difference and wavelength is inversely proportional. This means that as the wavelength increases, the path difference also increases, and vice versa. This is because longer wavelengths require a longer distance to complete one full cycle, resulting in a larger path difference between two waves.

4. Can path difference produce destructive interference for all types of waves?

Yes, path difference can produce destructive interference for all types of waves, including light waves, sound waves, and water waves. As long as two waves with the same frequency and a path difference of half a wavelength or more overlap, they will undergo destructive interference.

5. How is path difference related to the concept of phase difference?

Path difference and phase difference are closely related concepts. Path difference refers to the difference in distance traveled by two waves, while phase difference refers to the difference in the starting point of the two waves. In the context of destructive interference, a path difference of half a wavelength results in a phase difference of 180 degrees, causing the waves to be completely out of phase and cancel each other out.

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