471/Lectures/notes/lecture 32b Array thereom, gratings.pptx
Download
Report
Transcript 471/Lectures/notes/lecture 32b Array thereom, gratings.pptx
Array theorem and convolutions
N ik x xn y yn
Earray x , y , z e
* Eindividual x , y , z
n 1
aperture
Can derive array theorem from convolution theorem!
F g h ( x ', y ') 2 g x h x
Diffraction of the light
from a distant flashlight
viewed through a black
umbrella fabric.
2-slit Fraunhoffer diffraction pattern
Review: Sketch the diffraction
pattern of this rectangular slit
A) I got it mostly right
B) I got it mostly wrong but I tried
The E-field at the screen due to
one slit is (centered at the
origin)
ka kb
Eosinc x y
2 2
Sketch the E-field at the screen
due to due slits centered at y =
±h/2.
A) I got it mostly right
B) I got it mostly wrong but I tried
Earray
N ik x xn y yn
x , y , z e
* Eindividual x , y , z
n 1
aperture
N-slits diffraction features
How many minor peaks are
between the major peaks?
http://optics.byu.edu/animation/fraunhof.mov
N slits in a row, grooves,mirror-strips diffraction grating
N
e
n 1
i x x ' n
e
i
e
kh
x N
2
i
kh
x
2
e
i
kh
x N
2
e
i
kh
x
2
kh
sin N x
2
kh
sin x
2
h
sin N
2 a
I I peak sinc
N 2 sin 2 h
2
major peaks occur when ________ = m
a) 𝑁 𝜋ℎ 𝜃
b) 𝜋ℎ 𝜃
𝜆
𝜆
minor peaks occur when ________ = m
N-slits, grooves,mirror-strips diffraction grating
h
sin 2 N
2 a
I I peak sinc
N 2 sin 2 h
sin Nu
lim
u mult_
sin u
2
Ratio of major to minor peak in I:
a) N b) N2 b) N1/2
Width of major peak decreases as what power of N?
a) 1/N b) 1/N2 b) 1/N1/2
Diffraction grating orders
Diffraction grating orders
Blazed gratings put
more light into a
nonzero order
Reflective gratings are “blazed” to put
more light in order 1 than in order 0
Typical grating
for visible to UV
light: 1000-2000
grooves/mm, 10
cm wide105
lines.
Reflective gratings most common: lines cut in glass,
replicated onto plastic blanks, coated with metal (aluminum)
Modern methods
Resolving power of a grating
How much must change so peak moves by half its width?
h
sin N
2 a
I I peak sinc
N 2 sin 2 h
2
peak
RP
mN
Spectrometer
Put slits at f from mirrors.
Grating in center
What in the colors proves it’s
diffraction and not refraction?