Calculating Wavelength from Interference Pattern: Narrow Slits and Laser Light

[quicksilver123]

Homework Statement

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.

Homework Equations

| P_mS₁ - P_mS₂ |= m$\lambda$

The Attempt at a Solution

My answer:

|0.5000004-0.5000008|=(3)$\lambda$
0.0000004/3 = $\lambda$
$\lambda$ = 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$\lambda$
$\lambda$=0.00000135/3
$\lambda$=0.00000045m = 450nm

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

P_mS₁=0.50000030m
and
P_mS₂=0.50000165m

 

[TSny]

If the distance from one slit to the third bright fringe is 0.000004 m
and the distance from the other slit to the same bright fringe is 0.000008 m

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]

didn's leave anything out :/


sorry, i edited my original post a second ago.

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

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

How would I turn one into the other?

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