How Does Destructive Interference Occur at Point Q in a Double-Slit Experiment?

[foxtrot2]

Hello! I'm new here, and this is my first post. I hope I have not breached any rules, but here's a rather strange (in my limited intelligence) question I encountered. I shall try to explain the question because I am unable to reproduce the diagram.

Two identical narrow slits S1 and S2 are illuminated by light of wavelength (lambda) from a point source P.

[diagram = So, P (on the left) is connected to the line marked S1 and S2 by two lines l1 and l2. l1 is longer than l2. A point Q on the right of the line S1S2 is connected to S1 by l3 and S2 by l4, l3being longer than l4]

The light is allowed to fall on a screen (at Q), and if m is a positive integer, the condition for destructive interference at Q is that...

Thanks for the help!

EDIT: Crap, I just realized this is in the wrong thread... I really apologise for bungling up my first post and the inconvenience I have caused.

 

[Kazza_765]

Show us what you have tried already. Remember, for destructive interference the path difference must be equal to 1/2 or 3/2 or 5/2 or 7/2 etc wavelengths.

 

[quicknote]

Hello and welcome to the forum! Thank you for providing the diagram to help explain your question. From what I understand, you are asking about the conditions for destructive interference at point Q on the screen.

First, let's define what destructive interference is. It occurs when two waves of the same frequency and amplitude meet and their amplitudes cancel out, resulting in no net displacement. This can happen when two waves are out of phase with each other, meaning that their peaks and troughs do not line up.

In your setup, the point source P emits light of a certain wavelength (lambda) and it passes through two narrow slits S1 and S2. The light then travels to point Q on the screen. The lines l1, l2, l3, and l4 represent the paths that the light takes to reach point Q.

Now, the condition for destructive interference at point Q is that the path difference between the two waves coming from the two slits, S1 and S2, must be equal to an integer multiple of the wavelength (lambda). This means that the waves are perfectly out of phase with each other and their amplitudes will cancel out at point Q.

In your diagram, the path difference between the wave coming from S1 and the wave coming from S2 is represented by the difference in length between l3 and l4. And since l3 is longer than l4, this means that the path difference is equal to the difference in length between l3 and l4.

So, to answer your question, the condition for destructive interference at point Q is that the difference in length between l3 and l4 must be equal to an integer multiple of the wavelength (lambda). This can be expressed as (l3 - l4) = m(lambda), where m is a positive integer.

I hope this helps to clarify your question. Please let me know if you have any further questions or if I have misunderstood your question. Best of luck in your studies!