Determine horizontal separation of fabric from diffraction pattern

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SUMMARY

The discussion centers on calculating the horizontal separation of threads in a diffraction pattern. A participant initially questions whether a formula is necessary, suggesting a simple division of the horizontal distance (54.8 mm) by 2 to obtain 27.4 mm. However, it is established that a formula is required due to the nature of diffraction patterns. The correct formula involves using d sin θ = nλ, with specific values provided for λ (684 x 10-9 m) and y (27.4 x 10-3 m), leading to a calculated d of 5 x 10-5 m.

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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.
 
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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.
 
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Thank you very much haruspex
 

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