This preview shows page 1. Sign up to view the full content.
Unformatted text preview: φ/2) Don’t forget … The prelab is due at the beginning of lab !!
Lecture 4, p 27 Supplementary Slides Lecture 4, p 28 MultiSlit Interference
We already saw (slide 4) that the positions of the
principal maxima are independent of the number
of slits. Here, we will use phasors to determine
the intensity as a function of θ. y Incident wave
(wavelength λ) S3 A1 θ d
S2 At each principal maximum (d sinθ = mλ), the slits
are all in phase, and the phasor diagram looks like
this:
A1 P S1 L A1 Atot = N A1 à༎ Itot = N2 I1
For other values of θ, the phasors are rotated,
each by an angle φ with respect to its neighbors.
Remember that φ/2π = δ/λ = d/λ sinθ.
We can calculate Atot geometrically (next slide). Atot A1 φ A1
A1 φ Lecture 4, p 29 MultiSlit Interference (2)
The intensity for N equally spaced slits is found from phasor analysis.
Draw normal lines bisecting the phasors. They intersect, defining R as shown: φ R R
φ
2 φ
2 φ
2 φ
2 φ Substitute A1/2 N slits: R Nφ R A1
A1
φ
= R sin ⇒ R =
2
2
2sin (φ / 2 ) Atot Atot
Nφ
= R sin
⇒
2
2 Atot = A1
Itot Nφ
2 sin ( Nφ / 2 )
sin (φ / 2 ) ⎛ྎ sin(Nφ / 2) ⎞ྏ
= I1 ⎜ྎ
⎟ྏ
⎝ྎ sin(φ / 2) ⎠ྏ 2 φ A1 Lecture 4, p 30 Singleslit Diffraction
δa = a sinθ ≈ aθ To analyze diffraction, we treat it as interference of
light from many sources (i.e., the Huygens wavelets
that originate from each point in the slit opening).
Model the single slit as M point sources with spacing
between the sources of a/M. We will let M go to
infinity on the next slide. θ
a L The phase dif...
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.
 Spring '08
 Staff
 Quantum Physics, Diffraction

Click to edit the document details