# Determine horizontal separation of fabric from diffraction pattern

• songoku
In summary, the conversation is about using a formula to answer a question regarding a diffraction pattern. The formula d sin θ = nλ is used and assuming θ is small, the formula sin θ = y / L is derived where y is the horizontal distance and L is the distance between the screen and fabric. The final calculation gives a result of 5 x 10-5 m.
songoku
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

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

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.

songoku
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.

songoku
Thank you very much haruspex

## 1. How is the horizontal separation of fabric determined from a diffraction pattern?

The horizontal separation of fabric can be determined by measuring the distance between the peaks or valleys in the diffraction pattern. This distance is known as the diffraction spacing and is directly related to the spacing between the threads in the fabric.

## 2. What is a diffraction pattern?

A diffraction pattern is a pattern of light and dark bands that is produced when light passes through a regular pattern of small openings or obstacles. In the case of fabric, the diffraction pattern is created by the spaces between the threads in the fabric.

## 3. Why is determining the horizontal separation of fabric important?

Determining the horizontal separation of fabric is important because it can provide information about the quality and characteristics of the fabric. It can also help in identifying the type of fabric and its intended use.

## 4. What factors can affect the horizontal separation of fabric in a diffraction pattern?

The horizontal separation of fabric in a diffraction pattern can be affected by various factors such as the type of fabric, the thickness of the threads, the spacing between the threads, and the angle at which the light is passing through the fabric.

## 5. Can the horizontal separation of fabric be determined using other methods besides diffraction patterns?

Yes, the horizontal separation of fabric can also be determined using other methods such as microscopic analysis or physical measurements. However, diffraction patterns are often used because they are non-destructive and can provide quick and accurate results.

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