(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A laser with monochromatic light of frequency 6.33 × 10^14 Hz is fired through a diffraction grating.

If the first minimum in this diffraction pattern coincides with the position of the second order that was seen in the previous diffraction pattern, what is the width of the slit?

2. Relevant equations

[itex]w=\frac{\gamma}{\sin\theta}[/itex]

[itex]n\gamma=d\sin\theta_{n}[/itex]

3. The attempt at a solution

Here are my results from a previous question to which it refers

Using the following values: [itex]\gamma=633nm[/itex]

and [itex]\theta=39.3^{o}[/itex]

and the equation [itex]n\gamma=dsin\theta_{n}[/itex]

Rearranged for distance between the slits [itex]d=\frac{n\gamma}{sin\theta_{n}}[/itex]

then [itex]d=\tfrac{5*633x10^{-9}m}{sin(39.3)}=5\mu m[/itex] or 5.00E^{-6}m

Now to answer this question I've calculated the distance between the slits:

First calculate the distance between the slits second order using the equation [itex]d=\frac{n\gamma}{sin\theta} = \frac{2*633E^{-9}m}{sin(39.3)}=2\mu m[/itex] or 2.0E{}^{-6}

m.

This is where I don't know where to go... I know I need w... but how? Please help, I've had a thought:

by combining the two equations and substituting for [itex]\sin\theta[/itex] then maybe [itex]\frac{n\gamma}{d}=\frac{\gamma}{w}[/itex] so [itex]w=\frac{\gamma d}{n\gamma}=\frac{d}{n}[/itex]

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# Diffraction patterns and lasers!

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