A Brief History of Planetary Science - Augustana College
Double Slit Diffraction Physics 202 Professor Lee Carkner Lecture 27 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 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
Diffraction and Interference 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 ms (one for the diffraction and one for the interference) 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 ms) 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
Diffraction Envelope 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 ms 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 Diffraction Gratings
Get one maxima for each wavelength If we increase the number of slits (N) to very large numbers (1000s) 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 Maxima From Grating Diffraction Grating 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
Orders 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 Emission Lines of Hydrogen 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
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