Calculating Ym and R for Two-Slit Interference: Tips and Tricks"

[tj.]

Right so I've been stuck with this for a while now and I'm sure it's just something simple that I've missed. Right so the question says there are a pair of closely spaced slits (0.300mm apart). By changing the spacing the bright fringe moves from position m=2 to m=3. The wavelength remains constant. And that is all the information given in the question.



y_m=R(mλ/d)

So I've been given m and d but I don't have y_m or R (being the distance between the screen and the slits).



I would be very grateful if someone could be help find y_m or R. Thanks

 

[JesseC]

I suppose you could assume R is constant if the screen is far away relative to the slit spacing?

Perhaps you could reproduce the question in full, because it is slightly ambiguous at the moment. What is it asking you to work out?

 

[tj.]

Okay sorry:

'You shine a laser on a pair of closely spaced slits. By turning the knob, you can change the spacing of the slits. (The wavelength of the laser light remains constant.) Initially, the slits are 0.300mm apart.

You change the spacing of the slits so that the m=2 bright fringe moves to the position initially occupied by the m=3 bright fringe. What is the new spacing of the slits?'

 

[JesseC]

Well you don't need to worry about R, it is effectively constant over the region you're interested in (far field).

You might understand better what Ym is if you drew a picture of the experiment.

You can use the equation you wrote down for each different d:

$y_3 = 3 R \lambda / d_1$
$y_2 = 2 R \lambda / d_2$

I've just replaced m for its value for the two different slit widths. If you understand what Ym is you ought to be able to relate those two equations given what you've been told in the question?

 

[tj.]

Thanks JesseC! That's what it was, I was always trying to find a value for R. Thanks