E separating closely spaced spectral lines in n2i1 1

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 28.112° ⎝ྎ d ⎠ྏ −1 Small angle approximation is not valid. λ1 ⎞ྏ ⎛ྎ λ2 ⎞ྏ −1 ⎛ྎ Δθ = sin ⎜ྎ m ⎟ྏ − sin ⎜ྎ m ⎟ྏ = 0.031° ⎝ྎ d ⎠ྏ ⎝ྎ d ⎠ྏ −1 Lecture 4, p 17 Diffraction Gratings (1) Diffraction gratings rely on N-slit interference. They consist of a large number of evenly spaced parallel slits. An important question: How effective are diffraction gratings at resolving light of different wavelengths (i.e. separating closely-spaced ‘spectral lines’)? IN = N2I1 λ1 sinθ depends on λ. 0 λ1/d sin θ λ2 0 λ2/d sin θ Example: Na has a spectrum with two yellow “lines” very close together: λ1 = 589.0 nm, λ2 = 589.6 nm (Δλ = 0.6 nm) Are these two lines distinguishable using a particular grating? We need a “resolution criterion”. Lecture 4, p 18 Diffraction Gratings (2) We use Rayleigh’s criterion: The minimum wavelength separation we can resolve occurs when the λ2 peak coincides with the first zero of the λ1 peak: λ2/d λ1/d So, the Raleigh criterion is Δ(sinθ)min = λ/Nd. However, the location of the peak is sinθ = mλ/d. Thus, (Δλ...
View Full Document

This note was uploaded on 03/27/2014 for the course PHYS 214 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

Ask a homework question - tutors are online