How Do You Calculate the Width of a Slit Using Single-Slit Diffraction Data?

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To calculate the width of a slit using single-slit diffraction data, the relationship sin(θ) = mλ/a is essential, where λ is the wavelength of the laser light. The distance between the two intensity minima is measured at 17.9 millimeters, and the screen is positioned 80 centimeters from the slit. To find sin(θ), use the formula θ = y/x, where y is half the distance between the minima (8.95 mm) and x is the distance from the slit to the screen (800 mm). The value of m corresponds to the order of the minima, typically starting from m=1 for the first minimum. This approach allows for the calculation of the slit width a based on the measured parameters.
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Homework Statement


You have been asked to measure the width of a slit in a piece of paper. You mount the paper 80.0 centimeters from a screen and illuminate it from behind with laser light of wavelength 633 nanometers (in air). You mark two of the intensity minima as shown in the figure, and measure the distance between them to be 17.9 millimeters.

[PLAIN]http://img85.imageshack.us/img85/7453/101966.jpg

Homework Equations



sin(\theta)=m\lambda/a

Also for small angles \theta sin\theta = tan\theta = \theta

The Attempt at a Solution



I'm not really sure how to set up the equation. I'm used to having questions giving me the width of the central fringe and not the distance between 2 minima.

How do I use the given distance between the paper and screen and the distance between the two minima in the picture to calculate sin\theta

I'm also unsure what m would be equal to in this case.

Thanks
 
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Put θ = y/x, where y is the diatance of the mth dark fringe from the center and x is the distance between slit and the screen. In this problem it is 17.9/2 mm.
 

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