Two Slit Interference Question

[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.

Homework Statement

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?

Homework 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.

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?

Thanks in advance.

 

[benk99nenm312]

The assignment is graded and due tomorrow, can anyone please help?

 

[vela]

Looks right to me. I got the same answer.

 

[benk99nenm312]

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