Calculating Distance to Screen in Double Slit Diffraction Experiment

[solomar]

Homework Statement

Light of wavelength 460nm falls on two slits spaced .3 mm apart. What is the required distance from the slit to a screen if the spacing between the first and second dark fringes is to be 4mm?

Homework Equations

dsin(theta)=(m+1/2)lambda
where d = .3mm
y=4mm
lambda = 460nm
sin(theta)=y/L

The Attempt at a Solution

My problem is I don't understand what to use for m...delta m between the two dark fringes? (3/2-1/2), what am I supposed to use for m?
Using delta m I get:
L=dy/deltam*lambda
L=2.609 meters
Basically all I would really like to know is what in the world do I use for m?
also I am unsure if I am approaching this correctly, do I need to somehow incorporate approximation with small angles? If so, how?

 

[quanticism]

dsin(theta) = (m+1/2)(lambda)

So at m = 0, you get the first dark fringe. At m = 1, you get the second dark fringe.

I don't think "delta m" has any meaning in this context.

 

[solomar]

dsin(theta) = (m+1/2)(lambda)

So at m = 0, you get the first dark fringe. At m = 1, you get the second dark fringe.

I don't think "delta m" has any meaning in this context.

So then using those two values for m I would receive two different values for L. I don't see how having those two lengths solved would help me find the distance to the screen at all. I'm sorry I just don't understand how this leads to a solution...

 

[quanticism]

dsin(theta) = (m+1/2)(lambda)
d(y/L) = (m+1/2)(lambda)

Here, m gives you the "order" of the fringe, L is the distance from the slit and y is the vertical distance from the center of the screen to the dark fringe.

When you sub m=0 and all your known data in, you obtain an expression for y and L. Here, y is the distance to the first dark fringe.

Similarly, sub m=1 in and you obtain another expression involving y and L. This time, y is the distance to the second dark fringe.

The question gives you the separation between the first and second dark fringe so I'm sure you can work it out from there.

 

[solomar]

There we go! For some reason it wasn't quite clicking with me...but I definitely got it now, thank you very much :)