# Two Slit Interference Question

1. Mar 25, 2010

### benk99nenm312

Hey guys, I am trying desperately to figure this problem out. I have not done a problem like this ever before, and it is on our homework in a regular high school physics class. The teachers did not even teach us, this is just my attempt from research and previous knowledge.

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

Two narrow slits are spaced .25 mm apart and are 60 cm from a screen. what is the distance between the second and third bright lines of the interference pattern if the source is 546 nm of mercury?

2. Relevant equations

I used the equation y B (m) = (m$$\lambda$$L) / d , where y B (m) is the y coordinate of the bright spot on the interference pattern, m is the spot number (second or third spot), lambda is wavelength, L is the distance from the source to the screen, and d is the distance between the slits.

3. The attempt at a solution

I converted all given numbers to meters, then found the difference between the y coordinates of the 2nd and third bright spots. I called difference length, the variable we are looking for, x.

x = (3$$\lambda$$L) / d - (2$$\lambda$$L) / d
x = [3(5.46 x 10^-7 m)(.6 m) / (2.5 x 10^-4 m)] - [2(5.46 x 10^-7 m)(.6 m) / (2.5 x 10^-4 m)]
x = .0039312 m - .0026208 = a difference in the 2nd and third bright spot of .0013104 meters. But, that is barely a width of over a millimeter, I believe something went wrong. Can anyone please help?

2. Mar 25, 2010

### benk99nenm312

3. Mar 25, 2010

### vela

Staff Emeritus
Looks right to me. I got the same answer.

4. Mar 25, 2010

### benk99nenm312

Oh wow, sweet hah, the number just seemed a bit small to me. Thanks