# Single slit diffraction width

## Homework Statement

A single slit is illuminated with 630 nm light, and the resulting diffraction pattern is viewed on a screen 2.8 m away.
If the linear distance between the first and second dark fringes of the pattern is 12 cm, what is the width of the slit?

## Homework Equations

y=Ltan$$\theta$$
W = $$\lambda$$ m / sin $$\theta$$

## The Attempt at a Solution

theta = arctan (.12/2.8) = 2.45
W = 630 x 10^-9 x 2 / sin 2.45

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Doc Al
Mentor
Looks good.

I got 29.4 micrometers. It's wrong though.

Doc Al
Mentor
W = 630 x 10^-9 x 2 / sin 2.45
Oops... I missed that factor of 2 before. Why is it there?

Hint: Write expressions for the first dark fringe position and the second dark fringe position, then subtract.

I got it thank you so much!
I always get my "m" values wrong.