Path diffrence to produce destructive intefrence

[somecelxis]

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

Homework Equations

The Attempt at a Solution

 

[BvU]

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 ?

 

[NascentOxygen]

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?

 

[somecelxis]

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 .

 

[somecelxis]

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°) ...

 

[BvU]

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

 

[NascentOxygen]

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.

 

[somecelxis]

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?

 

[somecelxis]

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 ?

 

[somecelxis]

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 ?

 

[NascentOxygen]

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.

 

[BvU]

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...

 

[somecelxis]

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