# 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 Convert y =5 cm to tan = y/D, = arctan (y/D) = 0.52 deg Need to find to find I = (a/)sin = 10.5 rad

I = Im(sin/)2 = 0.007 Im Nearest minima What is m for our ? a sin = m m = (a sin / = 3.33

Between 3 and 4, closer to 3 Double Slit Diffraction In double slit interference we assumed a vanishingly narrow slit and got a pattern of equal sized (and equally bright) maxima and minima In single slit diffraction we produced a wide, bright central maximum and weaker side maxima

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 e.g. You would expect the m = 5 interference maxima would be bright, but if it happens to fall on the m = 3 diffraction minima it will be dark What you see at a certain angle , depends on both of the ms 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 For longer wavelengths the peaks are further apart

For solving diffraction/interference problems: Can find the interference maxima with d sin =m There are two different ms Intensity

= (a/) sin = (d/) sin The combined intensity is: I = Im (cos2 ) [(sin / ]2 Diffraction Gratings What happens when white light passes through a double slit? But each maxima is very broad and they overlap a lot

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 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 Using Gratings 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 Each element has a unique pattern of lines Emission Lines of Hydrogen Resolving Power and Dispersion What do we want from our grating?

Gratings with a high resolving power (R) produce narrow lines R = Nm D = m / (d cos ) Next Time Final Exam, Monday 9-11am Study, PAL, notes, old tests

Bring pencil and calculator