Diffraction
Light can “bend” around edges.
Each point of a “wave front” behaves as an independent
source of light.
• Produces no surprises for broad wave fronts without
obstacles.
Diffraction
Light can “bend” around edges.
Each point of a “wave front” behaves as an independent
source of light.
• Produces no surprises for broad wave fronts without
obstacles.
• Produces bend around obstacles.
Single Edge Narrow Gap
Diffraction
Light can “bend” around edges.
Significant when object dimensions are comparable to
wavelength.
Single Edge Narrow Gap
Single Slit Diffraction
Light passing through a narrow gap. Consider ray from
bottom of gap and ray from just above middle of gap.
y
θ
θ
Single Slit Diffraction
Destructive Interference
y
θ
θ
Single Slit Diffraction
For every ray from the lower half there is a
corresponding ray from the upper
completely out of phase
with the first ray at the
screen.
Single Slit Diffraction
The effect can be repeated for any even division of the
gap.
Destructive
Interference:
Single Slit Diffraction
Phase difference as a function of angle:
Intensity as a function of phase difference:
Example: 633 nm laser light is passed through a narrow slit
and a diffraction pattern is observed on a screen 6.0 m away.
The distance on the screen between the centers of the first
minima outside the central bright fringe is 32 mm. What is the
slit width?
Single Slit Diffraction
In Each of the Double Slits?
If the slit width is comparable to wavelength instead of
much smaller then one must also consider single slit
diffraction in the double slit experiment.
Diffraction Gratings
Derivation of maxima and minima similar to double slit.
More intense and sharper maxima.
Constructive Interference:
∆L
http://h2physics.org/?cat=49
Example: the wavelengths of visible light are from
approximately 400 nm (violet) to 700 nm (red). Find the
angular width of the first-order visible spectrum produced by a
plane grating with 600 slits per millimeter when white light falls
normally on the grating.
700 nm* 400 nm
angle?
Example: the wavelengths of visible light are from
approximately 400 nm (violet) to 700 nm (red). Find the
angular width of the first-order visible spectrum produced by a
plane grating with 600 slits per millimeter when white light falls
normally on the grating.
X-ray Diffraction
Regular spacing of atoms in a material can yield
pattern that can be used to determine the spacing.
Complex regular patterns in three dimensions can be
determined.
Resolving Power
If the minimum wavelength difference that can be
resolved by a diffraction grating is given by
then the resolving power is
where is the average of the two wavelengths.
It can be shown that
where is the number of slits and refers to the
th-order maxima.
Example: Light from mercury vapor lamps contain several
wavelengths in the visible region of the spectrum including two
yellow lines at 577 and 579 nm. What must be the resolving
power of a grating to distinguish these two lines?
mercury
Example: how many lines of the grating must be illuminated if
these two wavelengths are to be resolved in the first-order
spectrum?
mercury
Finding Maxima and Minima
Double slit maxima (constructive interference)
Single slit minima (destructive interference)
Diffraction grating maxima (constructive interference)
Intensity
Maximum intensity corresponds to constructive
interference (bright fringes).
Double slit
Phase difference: Intensity:
∆
Single slit
Phase difference: Intensity:
