Double Slit Help: 2nd Order Dark Fringe Location

[chrisahn97]

Homework Statement

A light source shines light of wavelength 490nm onto a pair of slits separated by 0.44m. Calculate the angular location and the location in cm of the second order dark fringes on a screen 1.4m from the slit

Homework Equations

Xn = (n-1/2)L lambda/d
delta x = L lambda/d

The Attempt at a Solution

So I understand how to find the angular location, but I don't understand why only one method for finding the location works. The method which works is using the formula containing Xn which gives the answer of 0.23cm. I don't understand why it is not possible given that this is double slit to use delta X = L lambda/d then multiply that answer by 2 to get your answer as it gives a different value.

X₂=(2-1/2)(1.4)(4.9x10^-7)/0.44x10^-3 = 0.23cm (the answer in the back of the textbook)

Using ΔX = Lλ/d
ΔX = (1.4)(490x10^-9)/0.44x10^-3
= 0.0015
as it is to the second dark fringe, shouldn't 0.0015x2 get me the same answer as my previous Xn calculation?

 

[Orodruin]

Please show your work step by step.

 

[TSny]

Homework Statement

A light source shines light of wavelength 490nm onto a pair of slits separated by 0.44m. Calculate the angular location and the location in cm of the second order dark fringes on a screen 1.4m from the slit

Is the sit separation supposed to be 0.44 mm?

Homework Equations

Xn = (n-1/2)lambda/d
delta x = L lambda/d

Should the first equation have a factor of L?

The Attempt at a Solution

So I understand how to find the angular location, but I don't understand why only one method for finding the location works. The method which works is using the formula containing Xn which gives the answer of 0.23cm. I don't understand why it is not possible given that this is double slit to use delta X = L lambda/d then multiply that answer by 2 to get your answer as it gives a different value.

Think about the meaning of "delta x" and think about the meaning of X_n. In particular, "delta x" represents the distance between what two points? X_n represents the distance between what two points?

 

[chrisahn97]

I thought it wasn't necessary as it was more an issue with the concept as I was able to reach the correct answer on my own using the Xn formula, so sorry!
Updated

 

[NascentOxygen]

Hi chrisahn97. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

Sketch the expected pattern of fringes, and mark in those 2 distances precisely using dimensioning lines such as:

|<--------------- X_n --------------->|

 

[Orodruin]

Is the first dark fringe a distance Δx away from the center? If not, should the second dark fringe be a distance 2Δx away?

 

[chrisahn97]

Is the first dark fringe a distance Δx away from the center? If not, should the second dark fringe be a distance 2Δx away?

oh I see now thank you!
I think my method would have only worked if the question was asking for the second bright fringe, as the distance from the central maximum to the first dark band would not be delta X but would be 1/2ΔX

 

[Orodruin]

Yes. In fact, this is how you would derive your other formula, which gives the location of an arbitrary dark fringe.

 

[chrisahn97]

Careless error on my part thanks for the help. This question can be marked as solved if that's a thing on these forums