# An interference question

## Homework Statement

http://img337.imageshack.us/img337/285/64902163.png [Broken]

## Homework Equations

$$\Delta x = \frac{\lambda L}{d}$$
where delta x is the fringe separation
L is the distance from screen to signal source
d is the slit separation

## The Attempt at a Solution

Okay you see I'm using the equation from the double-slit experiment (should I?) But I cannot draw an analogy between double-slit experiment and the situation here. Am I on the right track?

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vela
Staff Emeritus
Homework Helper
No, you don't want to use that equation. You don't have interference due to waves emanating from two slits in this problem, so that formula doesn't apply.

You get maxima and minima because of waves interfering, and to get interference, you have to have two waves reaching M. So the first step is determining what the two path waves follow to go from S to M.

No, you don't want to use that equation. You don't have interference due to waves emanating from two slits in this problem, so that formula doesn't apply.

You get maxima and minima because of waves interfering, and to get interference, you have to have two waves reaching M. So the first step is determining what the two path waves follow to go from S to M.

Okay, I suppose that there's a wave going from S to M directly and the wave reflected from the screen.

Actually I've been thinking along the line about treating the reflected wave as one emanating from a fictitious source situated behind the screen, symmetrical to S. Then the minima would be akin to having a dark fringe on M. That should work as well?

vela
Staff Emeritus
Homework Helper
Yeah, that should work, I think.

Okay I need more help because I still cannot get the answer. (The supposedly correct answer is A by the way.)

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vela
Staff Emeritus
Homework Helper
One wave has to travel 12 cm to go from S to M. The other one travels a bit more because it reflects from the wall. Calculate the difference in path length for the two waves. If they differ by a half wavelength, you'll get destructive interference.

okay cool i got it thanks :D

ehild
Homework Helper
Is no phase change at the wall?

ehild

during reflection the phase changes by 180°, but that should be quite irrelevant to solving this question since we're only interested in the overall path difference.

ehild
Homework Helper
No, we are interested in the overall phase difference.

ehild

vela
Staff Emeritus
Homework Helper
Good point. I totally forgot about the phase change at the screen.

ehild
Homework Helper
I just wondered what happens if the screen is made from some elastic material?

ehild

Did you guys get the answer A?

ehild
Homework Helper
Yes, if there is a pi phase change at the screen.

But that speaker should be a bat...

ehild