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?  a sin   = and a sin   = 2 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 m 2 = (0.25 X )(1.625 X )/650 X = 6.25 

PAL #27  Middle interference fringe is m = 5    = (  a/  sin  = [(  )(0.08 X ) /(650 X )] (0.013) = rad   = (  d/ ) sin  = [(  )(0.25 X ) /(650 X )] (0.013) = rad  I = I m cos 2  (sin  /  ) 2 = I m (1)(0.0358) = I m

Diffraction Gratings  For double slit interference the maxima are fairly broad   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 and is useful for spectroscopy

Maxima From Grating

Diffraction Grating

Grating Path Length

Location of Lines  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.  For polychromatic light each maxima is composed of many narrow lines (one for each wavelength the incident light is composed of)

Grating Orders

Line Width   The half-width (angular distance from the peak to zero intensity) of a line is given by:   where N is the number of slits and d is the distance between 2 slits

Line Profile

Spectroscopy  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   This is how the chemical compositions of stars are determined

Spectroscope   This will produce a series of orders, each order containing lines (maxima) over a range of wavelengths   The wavelength of a line corresponds to its position angle   We measure  with a optical scope mounted on a vernier position scale 

Spectroscope

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:  For larger m and smaller d the resulting spectra takes up more space

Dispersed Spectra

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 R = av /    For example, a grating with R = could resolve 2 blue lines (  = 450 nm) that were separated by nm

Dispersion and Resolving Power

Resolving Power of a Grating  R = Nm  Gratings with large N are the best for spectral work 