Determine horizontal separation of fabric from diffraction pattern

AI Thread Summary
Determining the horizontal separation of fabric from a diffraction pattern requires using a specific formula rather than simply dividing the horizontal distance by two. The discussion emphasizes that the diffraction pattern is complex and not a straightforward projection. The formula d sin θ = nλ is applicable, where θ is small, and sin θ can be approximated as y / L, with y being the horizontal distance from the central maxima and L the distance to the screen. The calculations provided by the user, leading to a separation of 5 x 10^-5 m, are confirmed as correct. Understanding the distinction between horizontal and vertical measurements is crucial in this context.
songoku
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Homework Statement
When a laser of 684 nm wavelength is incident on a fabric, a diffraction pattern is observed on a screen placed at a distance of 2 m away as shown below. Determine the separation between horizontal threads of the fabric
Relevant Equations
d sin = n λ
1616384584868.png


Do I need to use formula to answer this question? Can't I just divided the horizontal distance in the picture by 2. so the horizontal separation of the thread is 54.8 / 2 = 27.4 mm?

Thanks
 
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songoku said:
Do I need to use formula to answer this question? Can't I just divided the horizontal distance in the picture by 2. so the horizontal separation of the thread is 54.8 / 2 = 27.4 mm?

Thanks
It's a diffraction pattern, not a simple projection. Yes, you need to use the formula.
 
haruspex said:
It's a diffraction pattern, not a simple projection. Yes, you need to use the formula.
Is formula for horizontal separation the same as vertical distance? What I learned so far is all about vertical distance measured from central maxima.

My attempt:
d sin θ = nλ and assuming θ is small, then sin θ = y / L where y is the horizontal distance measured from central maxima and L is distance between screen and the fabric.

Taking n = 1 :
d sin θ = nλ
d y / L = λ
d = L . λ / y = 2 (684 x 10-9 / (27.4 x 10-3) = 5 x 10-5 m

Is this correct? Thanks
 
Last edited:
songoku said:
Is formula for horizontal separation the same as vertical projection? What I learned so far is all about vertical distance measured from central maxima.

My attempt:
d sin θ = nλ and assuming θ is small, then sin θ = y / L where y is the horizontal distance measured from central maxima and L is distance between screen and the fabric.

Taking n = 1 :
d sin θ = nλ
d y / L = λ
d = L . λ / y = 2 (684 x 10-9 / (27.4 x 10-3) = 5 x 10-5 m

Is this correct? Thanks
Looks right.
 
Thank you very much haruspex
 
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