[MuZI]

Here is a homework problem that seems to have me stumped, any help?


"In Young’s double-slit experiment, suppose that the slit separation is precisely equal to the wave length of the light used. In this case, the interference pattern on the screen would be a) pattern of bright and dark fringes so closely spaced as to be imperceptible, b) pattern of one central bright fringe and two dark fringes only, c) completely bright screen with no dark fringes, or d) completely dark screen."

So I know for multiple slit we have d*sin(theta)=m(lambda) where m is an integer for constructive interference... that's all I have so far.

 

[gates_2]

yay for physics(taking it over the summer right now)

so you know that the slit separation, d is equal to the wavelength, right?

thus, the lambda and d will cancel, leaving you with sin theta = M, the principal number

well, sin theta can never be greater than 1 right? and the lowest value of M is M=1, so if you are looking at the principal maxima for M=1, then the theta is going to be 90 degrees, and the light will be completely refracted, thus giving you a completely dark screen, or answer D

*I'm not 100% sure on this, and this is just an initial idea*

 

[MuZI]

Hmm, yeah I agree with you up until sin (theta) = m

But you can have M = 0 (first bright spot right in the middle) and M = 1/2 (first dark spot?) right?


I think I just answered my own question 1 bright spot in the middle... 2 dark spots on either side... B?

 

[circularlogic]

Well, the central maximum will be at the center, so there will have to be some light. However when m=1, the next maximum will occur when sin(theta)=1, which is infinity, since the angle of the light producing the next maximum will be parallel to the screen.

However! That makes both answer b and c plausible, since it depends on how big the screen is, if it's infinitely long, you'll see the light fade away and make the other two dark bands. If relatively short, you should just see a completely bright screen, even if the brightness isn't constant.

I'd go with b, since the fading edges can be interpreted as dark I guess?

 

[gates_2]

mm- yes, i'm not sure why i was thinking that the lowest value of M is 1(it is 0, of course)

I'd agree with the answer B

 

[steaxauce]

I say B.

There won't be a completely dark spot anywhere on the screen, because the waves from the two slits won't cancel until they're at 90 degrees from the center, but there will be a central bright spot and it will get darker as you go out to the edges.