slit & light interference

quicksilver123

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

Two narrow slits are cut into a sheet of paper and set in front of a laser beam, causing an interference pattern to appear on the wall.
If the distance from one slit to the third bright fringe is 0.5000004 m
and the distance from the other slit to the same bright fringe is 0.5000008 m
calculate the wavelength of the light from the laser.

2. Relevant equations

| P_mS₁ - P_mS₂ |= m[itex]\lambda[/itex]

3. The attempt at a solution

My answer:

|0.5000004-0.5000008|=(3)[itex]\lambda[/itex]
0.0000004/3 = [itex]\lambda[/itex]
[itex]\lambda[/itex] = 0.000000133 m

edit: my answer uses
| P₃S₁ - P₃S₂|
whereas the book's answer uses
| P_mS₁ - P_mS₂|

How would I turn one into the other?

The book's answer:

|0.50000030-0.50000165|=3[itex]\lambda[/itex]
[itex]\lambda[/itex]=0.00000135/3
[itex]\lambda[/itex]=0.00000045m = 450nm

I'd like to know where they got the values of:

P_mS₁=0.50000030m
and
P_mS₂=0.50000165m

TSny

Did you leave out the "5" after the decimal points? Your work looks correct to me. I don't see where the book's numbers come from either.

quicksilver123

didn's leave anything out :/


sorry, i edited my original post a second ago.


edit: my answer uses
| P3S1 - P3S2|
whereas the book's answer uses
| PmS1 - PmS2|

How would I turn one into the other?

TSny

Is the distance from the first slit to the bright fringe 0.000004 m or 0.500004 m?

Let m = 3?

quicksilver123

sorry, corrected the mistake.

the book has been known to make errors in their solutions... but i was wondering if there's something i'm missing

TSny

I think your work is correct.

quicksilver123

alright, thanks