Diffraction Applications Physics 202 Professor Lee Carkner Lecture 28

PAL #27  What is in the first side pattern in a double slit set-up with a = 0.08 mm and d = 0.25 mm and l = 650 nm?  The first side pattern is between the m=1 and m=2 diffraction minima: sin   = /a and sin   = 2 /a sin  2 = (2)(650 X )/0.08 X =1.625 X 10 -2

PAL #27  What interference maxima are between the two angles? d sin  1 =m 1 and d sin  2 = m 2 m 1 = (0.25 X )(8.125 X )/650 X = 3.13 

PAL #27  Middle interference fringe will be brightest (m = 5)  sin  = (5)( )/(d) = (5)(650 X )/ 0.25 X =    = (  d/ ) sin  = [(  )(0.25 X ) /(650 X )] (0.013) = rad 

Spectroscopy  In a hot material (e.g. a gas) composed of atoms will emit light due to electrons changing energy levels   Gratings are used to separate light into its constituent wavelengths in order to identify this light as spectral lines  The positions and strengths of these lines are unique for specific elements 

Spectroscope  We want to pass the light through a grating  This will produce a series of orders, each order containing lines (maxima) over a range of wavelengths    We measure  with a optical scope mounted on a vernier position scale  Can also take an image of the pattern

Spectroscope

Grating Orders

Spectral Type   This is how the temperature of stars is determined  Examples:   Stars like the Sun (T~5500 K) can be identified by the Ca h and k doublet which is only produced at moderate temperatures

Using Spectroscopy  What properties do we want our spectroscope grating to have?    How can we achieve this?

Dispersion  The size of the spectrum (from short to long ) produced by a grating is a function of the dispersion, D:  The dispersion can also be written: 

Resolving Power  The most important property of a grating is the resolving power, a measure of how well closely separated lines (in ) can be distinguished  where av is the average wavelength of two lines 

Dispersion and Resolving Power

Resolving Power of a Grating  The resolving power depends on the number of rulings and the order:   Note that large N means that d might be small which will increase D