Determine horizontal separation of fabric from diffraction pattern

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Homework Help Overview

The discussion revolves around determining the horizontal separation of fabric based on a diffraction pattern. Participants are exploring the relationship between horizontal and vertical measurements in the context of diffraction, particularly focusing on the application of relevant formulas.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Some participants question whether a formula is necessary for calculating horizontal separation, suggesting a simple division of distance. Others emphasize the need for a formula due to the complexity of diffraction patterns. There is also inquiry into whether the formula for horizontal separation is analogous to that for vertical distance, with attempts to apply the diffraction equation d sin θ = nλ.

Discussion Status

Participants are actively discussing the application of formulas and the assumptions involved in measuring horizontal versus vertical distances in diffraction. Some guidance has been offered regarding the necessity of using formulas, and there is acknowledgment of the attempts made to apply the diffraction equation correctly.

Contextual Notes

There is a focus on the distinction between horizontal and vertical measurements in the context of diffraction, with references to specific distances and wavelengths. Participants are working within the constraints of their current understanding of diffraction patterns and the associated formulas.

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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