Homework Help: Single slit help?

1. Feb 21, 2013

alittlelost

1. The problem statement, all variables and given/known data

A beam of light of unknown wavelength is incident on a screen with a single-slit. Observing the interference pattern on the projection screen that is 1.7 m away, the 4th minimum is 27 cm away from the central line. The width of the slit is 15 μm.
a) What is the wavelength (in nm) of the light used?

b) How wide(in cm)is the central maximum?

2. Relevant equations
Single slit equations

3. The attempt at a solution
I plugged everything in, stuck on the first step.

Xn= n*Lλ/w
= 4*1.7λ/1.5x10-5

Help?

2. Feb 21, 2013

TSny

Hello, alittlelost.

To me, it's not clear what you're stuck on. Are you having trouble doing the math steps to solve for λ or is it something else?

3. Feb 21, 2013

alittlelost

Hey TSny, actually that is what I'm having trouble with. My brain is absolutely fried. It's probably so simple, but I can't seem to figure it out right now.

4. Feb 21, 2013

TSny

If you have the equation a = x/b and you need to solve for x, what would you do?

5. Feb 21, 2013

alittlelost

divide a by b to isolate x?

6. Feb 21, 2013

TSny

No. Consider a simple equation where you can easily see what the answer should be. Such as 4 = x/2

7. Feb 21, 2013

alittlelost

Well for that I would just multiply the 4 and 2 to find x...Sorry, I misread. I'm a little tired. I just don't know how to rearrange this equation to find λ.

8. Feb 21, 2013

TSny

Good. So to solve 4 = x/2 you multiply both sides by the denominator 2. Going back to your equation for λ, what would you multiply both sides by?

9. Feb 21, 2013

alittlelost

by 1.5x10-5?

So it should look like this then?

(4)(1.5x10-5) = (4)(1.7)(1.5x10-5

10. Feb 21, 2013

TSny

Not quite. Let's work in symbols before plugging in numbers.

You have the equation X = n*L*λ/w. What does this become after you multiply both sides by w? (Note that I wrote your symbol Xn as just X because I think Xn looks like X multiplied by n which could get confusing.)

Last edited: Feb 21, 2013
11. Feb 21, 2013

alittlelost

You would get X*w= n*L*λ right?

12. Feb 21, 2013

TSny

Yes. Good. Now you need to isolate λ. How are you going to (legally!) "get rid" of n and L on the right?

13. Feb 21, 2013

alittlelost

Could I move n and L to the other side of the equation?

14. Feb 21, 2013

TSny

Yes! Can you think of something you an do to both sides of the equation so that n and L disappear on the right and appear on the left?

15. Feb 21, 2013

alittlelost

Divide both sides by n and L which would cause them to disappear?

16. Feb 21, 2013

TSny

Right, that will cause n and L to disappear on the right and appear somewhere on the left. Then you can evaluate λ.

17. Feb 21, 2013

alittlelost

Since I'm bringing over n and L they would become negative on the left side correct?

18. Feb 21, 2013

TSny

No, dividing both sides by n and L does not cause n and L to change sign.

If you wanted to solve a = x*b for x, you would divide both sides by b to get a/b = x. Note that b does not change sign.

19. Feb 21, 2013

alittlelost

after everything gets cancelled out, should I only have X*w =λ? If so, I got 60000nm

Last edited: Feb 21, 2013
20. Feb 21, 2013

TSny

No that's not the correct formula for λ. Remember, if you solve a = x*b for x by dividing both sides by b, you get a/b = x. So, the b disappears on the right, but it now shows up on the left.

So, when you divide both sides of X*w = λ*L*n by L and n, L and n will then appear somewhere on the left side. On the left side you will have an expression that represents dividing X*w by L and n.

21. Feb 21, 2013

alittlelost

Ugh, so close to giving up on this one :p too tired.. I divided 4*1.5*10-5 by 4*1.7 and I got 8820nm.. is that correct?

22. Feb 21, 2013

TSny

Ok, I think you are very close! So, after dividing both sides of X*w = λ*L*n by L and n you get X*w/(n*L) = λ, or

λ = X*w/(n*L)

Looks like you substituted 4 for X, as shown in red above. That's not correct. Do you know what the symbol X stands for? It's value is stated in the problem. Otherwise, your calculation looks correct.

23. Feb 21, 2013

alittlelost

According to my notes it's the 4th minimum that's 27cm from the central line.. I was supposed to plug in 0.27m wasn't I...

24. Feb 21, 2013

TSny

Yes.

25. Feb 22, 2013

alittlelost

Okay, I got 596nm... did I finally get it?