Double Slit Diffraction Physics 202 Professor Lee Carkner Lecture 27.
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Transcript of Double Slit Diffraction Physics 202 Professor Lee Carkner Lecture 27.
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Double Slit Diffraction
Physics 202Professor Lee
CarknerLecture 27
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PAL #26 Diffraction Single slit diffraction, how bright is spot 5 cm from
center? = 680 nm, a = 0.25 mm, D = 5.5 m tan = y/D, = arctan (y/D) = 0.52 deg = (a/)sin = 10.5 rad I = Im(sin/)2 =
Nearest minima What is m for our ? m = (a sin / = 3.33
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Double Slit Diffraction
Each maxima had the same peak intensity
Double slit diffraction produces a pattern that is a combination of both The interference maxima are modulated in
intensity by a broad diffraction envelope
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Diffraction and Interference
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Double Slit Pattern The outer diffraction envelope is defined by:
a sin =m
Between two minima, instead of a broad diffraction maxima will be a pattern of interference fringes
d sin = m a,d and are properties of the set-up, indicates a
position on the screen and there are two separate m’s (one for the diffraction and one for the interference)
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Patterns What you see on the screen at a given spot depends on both
interference and diffraction
Remember that a location in the pattern is defined by
We can use the location of two adjacent diffraction minima (sequential diffraction m’s) to define a region in which may be several interference maxima
i.e. first define the diffraction envelope, then find what interference orders are inside
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Diffraction Envelope
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Diffraction Dependencies
For large (d) the interference fringes are narrower and closer together
In an otherwise identical set-up a maxima for red
light will be at a larger angle than the same maxima for blue light
For solving diffraction/interference problems: Can find the interference maxima with d sin
=m There are two different m’s
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Intensity
The intensity in double slit diffraction is a combination of the diffraction factor:
and the interference factor:
The combined intensity is:
I = Im (cos2 ) [(sin / ]2
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Diffraction Gratings
Get one maxima for each wavelength
If we increase the number of slits (N) to very large numbers (1000’s) the individual maxima (called lines) become narrow
A system with large N is called a diffraction grating Used for spectroscopy, the determination of a
materials properties through analysis of the light it emits at different wavelengths
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Maxima From Grating
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Diffraction Grating
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Location of Lines
The angular position of each line is given by:d sin = m
The m=0 maxima is in the center, and is flanked by a broad minima and then the m=1 maxima etc.
Called an order
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Orders
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Resolving Power and Dispersion
Narrow lines that are well spread out
R = Nm
D = m / (d cos ) To get a large resolving power and
dispersion want a grating with many slits that are very close together
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Emission Lines of Hydrogen
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Using Gratings Heat up a gas that is composed of a certain
element (e.g. hydrogen) and pass the light through a grating
Rather than a continuous spectrum of all colors, the gas only produces light at certain wavelength called spectral lines
By passing the light through a grating we can see these spectral lines and identify the element