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

A visible light spectrometer has a grating of width D=10cm and a collimating lens of focal length L=1m. Show that the optimal width for the input slit is such that it will produce a diffraction pattern of width D.

2. Relevant equations

The diffraction pattern of a single slit of width b is given by [tex]I*Sinc(\beta)[/tex]

Where [tex]\beta = \frac{kb}{2}[/tex]

k is the wave number.

3. The attempt at a solution

I really have no idea where to begin here. I understand that the purpose of a collimator lens is to send parallel rays of light to the diffraction grating, so wouldn't that mean it would require an image of 0 width at it's focal point? So shouldn't the slit be made as small as possible?

The only other thing I can think of is this has to do with the dependence of the diffraction pattern on the wavelength of light. Is the slit supposed to diffract the light before it reaches the diffraction grating or something?

I'm completely lost and have been going in circles for hours so any help would be appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Spectrometer slit width

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**