1. Diffraction Applications Physics 202 Professor Lee Carkner Lecture 28

2. 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 10 -9 )/0.08 X 10 -3 =1.625 X 10 -2

3. 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 10 -3 )(8.125 X 10 -3 )/650 X 10 -9 = 3.13 

4. PAL #27  Middle interference fringe will be brightest (m = 5)  sin  = (5)( )/(d) = (5)(650 X 10 -9 )/ 0.25 X 10 -3 = 0.013    = (  d/ ) sin  = [(  )(0.25 X 10 -3 ) /(650 X 10 -9 )] (0.013) = 15.71 rad 

5. 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 

6. 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

7. Spectroscope

8. Grating Orders

9. 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

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

11. 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: 

12. 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 

13. Dispersion and Resolving Power

14. 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