# Find the distance between the two third order maxima

1. May 7, 2006

### Spruance

Red light with wavelength 713 nm pass through a double split with "split distance" 0.120 mm. The interference pattern gets observed on a screen that is 2.75 m from the double split. Find the distance between the two
third order maxima we seeing on the screen.

(My english is really awkward)

2. May 7, 2006

3. May 7, 2006

### Spruance

d sin 0 = n*lambda

sin 0 = ((n*lambda)/d) = (3 * 713 * 10^-9 m/ 0.120 * 10^-3 m) = 0.017825 = Sin (1.02)

tan 0 = y/r = y/2.75 m

y = tan 1.02 * 2.75 m = 2.80 m

4. May 7, 2006

### Staff: Mentor

Recheck that last step. (Note that for small angles, tan(theta) = sin(theta))

You have caculated the position of the 3rd order maximum from the central position (where y = 0), but the problem asks for the distance between the two 3rd order maxima. Where's the other one?

5. May 7, 2006

### Spruance

I don't got any answer-book, but I am sure that my previous answer is wrong.

6. May 7, 2006

### Spruance

I really don't know what I have to do ...

Last edited: May 7, 2006
7. May 7, 2006

### Staff: Mentor

You multiplied by 1.02 instead of tan(1.02). (1.02 is degrees, by the way.)

8. May 7, 2006

### Spruance

y = tan 1.02 * 2.75 m = 0.04896 m

It cannot be correct

9. May 7, 2006

### Hootenanny

Staff Emeritus
I hope Doc Al doesn't mind me jumping in here, but he seems to be else where. You have calculated the distance between the normal (zero order beam) and the third order beam. The question asks you to calculate the distance between the two third order beams.

HINT: You are half way there.

~H

10. May 8, 2006

### Spruance

Sin 0 = (n*lambda)/d = ((3 * 713 *10^-9)/(0.120 * 10^-3)) = 0.018

Sin 0.018 = 1.047

Sin 1.047 = (x/2.75)

x = Sin 1.047 * 2.75 m

x = 0.050 m

11. May 8, 2006

### Hootenanny

Staff Emeritus
I'm not sure what your doing here, in any case it is incorrect, $\sin\theta$ only equals zero when n = 0, i.e. the zero order beam. Alarms bells should have started ringing when you abtained sin 0 = a non zero number. You were very close with your previous answer. BIG HINT: The interference pattern is symetrical about the zero order beam (y=0).

~H

12. May 8, 2006

### Spruance

sin theta = (n*lambda)/(d)

= (3*713 * 10^-9)/(0.120 * 10^-3)

= Sin(0.017825) = 1.02135136

tan (1.021) = (x/2.75)

x = tan 1.021 * 2.75 = 0.049

0.049 * 2 = 0.098 m

13. May 8, 2006

### nrqed

?? How do you get from the first line to the second line??
What do you get for the first line??

14. May 8, 2006

### Spruance

I belive that if you just put the numbers into a calculator, it gives you that (3*713 * 10^-9)/(0.120 * 10^-3) is 0.017825

Invers sinus of 0.017825 is the same as Sin(1.02)

15. May 8, 2006

### nrqed

Sorry.. I had used 0.1 mm. You are correct. My apologies

16. May 8, 2006

### nrqed

This is correct...

17. May 8, 2006

### Hootenanny

Staff Emeritus
Just for reference, the same result can be obtained by simply doubling this number because (as I said earlier) the interference pattern is symmetrical around the zero order beam.

~H