# Homework Help: Diffraction grating - have answer and working, but don't understand it

1. Nov 15, 2007

### karnten07

1. The problem statement, all variables and given/known data

A sodium lamp with wavelength 589nm is diffracted by the fabric of an umbrella with a spacing of 0.04mm. If the sodium lamp is 20cm across and 100m from the umbrella, by how many multiples of the lamp width will the diffraction order, viewed through the fabric of the umbrella, appear to be displaced.

2. Relevant equations
Theta = arcsin (wavelength/d)

where d is the line spacing, 4 x10^5 m in this case

3. The attempt at a solution

It was found that the first order diffraction angle is 0.84 degrees using the equation above.
I have the answer and working here but don't understand what the question is asking:

The lamp subtends (0.2 x 180)/(100 x pi) = 0.11 degrees

Diffracted order subtends 0.84/0.11 = 7.4 lamp widths.

If anyone can explain what is going on here it would be greatly appreciated.

Last edited: Nov 15, 2007