Young's double-slit interference?

[kimlu]

Homework Statement

In a Young's double-slit experiment, a set of parallel slits with a separation of 0.102 mm is illuminated by light having a wavelength of 580 nm and the interference pattern observed on a screen 4.50 m from the slits.
(a) What is the difference in path lengths from the two slits to the location of a second order bright fringe on the screen?
(b) What is the difference in path lengths from the two slits to the location of the second dark fringe on the screen, away from the center of the pattern?

Homework Equations

x/L = λ/d
x= 2λL/d

3. The Attempt at a Solution

2(580E-9)(4.5)/ (.000102)= .051m

I'm supposed to have it in µm and I put 51,176 but I kept getting the question wrong, what am i doing wrong?
Also for the second part I am confused on fringes since its the 2nd dark fringe does that mean the 2nd fringe that is dark which is between the 1st and 2nd order bright or a dark fringe that is 2 which is between the 3rd and 4th order bright. Am i even thinking about this the right way, each dark fringe is 1/2λ correct?

 

[mfb]

You calculated the distance between things on the screen (and got the conversion m -> µm wrong), that's not what you are supposed to calculate.

The differences in path lengths are comparable to the wavelength.

Am i even thinking about this the right way, each dark fringe is 1/2λ correct?

1/2λ is just one option.

 

[kimlu]

thanx

 

[Phil Lawless]

Do a search on "Quantum interference with slits" by Thomas Marcella. It is in arxive.org. It gives a full quantum analysis of the two-slit geometry.

 

[berkeman]

Do a search on "Quantum interference with slits" by Thomas Marcella. It is in arxive.org. It gives a full quantum analysis of the two-slit geometry.

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