Physics
posted by ####Nadine#### on .
When violet light of wavelength 415 nm falls on a single slit, it creates a central diffraction peak that is 8.80 cm wide on a screen that is 2.75 m away. How wide is the slit?

Is there something wrong with this? http://www.jiskha.com/display.cgi?id=1335108759 The part poorly defined is the "peak that is ...wide". The formula I gave you is the distance to the first minimum.
Some folks use the "width " of the peak to not the first minimum, but to the point where the peak has went down to the .707 RMS value. 
I skipped over this question because I was not sure what was meant by width of the stripe. I think first minimum is most common.

The width of the central peak (max) is the distance between the first minima.
The equation for diffraction minima is
b•sinφ = k•λ.
k =1,
b = λ/sinφ.
From the geometry of diffraction pattern
tanφ =x1/L,
where x1 =8.8/2 = 4.4 cm =0.044 m is the distance between the center of diffraction pattern and the first min,
and L =2.75 m.
tan φ = 0.044/2.75=0.016.
sin φ = tan φ=0.016.
b = λ/sinφ = 415•10^9/0.016 =
=2.59•10^5 m =25.9 micrometers. 
Thank you so much Elena! I forgot to divide 8.8 by two and, of course, kept getting double the answer which I knew was incorrect.

Anyone else from SF have to google this question, or was i the only one?