4.3 Measuring the Width of Diffracting Objects
The numerical relationship between the width of a slit or hair and wavelength
can be measured using the laser with the lens in place to produce an intense
parallel beam. The relationship between the width of the central diffraction
maximum and wavelength can also be investigated.
Light intensity
incident
light
W
d

L
Figure 4.9 Single slit diffraction to show /W relationship
Activity
Do not stare at the laser beam
Beware of reflections
View the laser from above,
Use card or a screen to trace the path of the laser beam
Set up the laser beam and slit so that a diffraction pattern is seen on the
monitor. The wavelength of the laser is given as 650nm. Note the
spectrometer could be set up to confirm the wavelength.
Laser with Lens
Slit
Screen
Figure 4.10 Measuring diffraction patterns
A piece of paper may be used in place of the screen using a pen to mark out
the position and size of the central maxima.
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Use the equation to calculate the width of the slit, d. W is the width of the
central maximum,  is laser wavelength and L the distance from the screen to
slit.
2 L
d
W
A relationship exists between the wavelength, angle to the first maximum of
constructive interference and width of diffracting object.
Light intensity
incident
light
d
n=1

n=0

n=1
L
Figure 4.11 Measuring d using the first maxima.
Set up the laser beam so it is interrupted by a wire or hair and a good
diffraction pattern is seen on the screen. Measure the distances as before and
calculate the width of the hair by reference to figure 4.11 and using
n  dSin
Do you think the same calculations apply to diffraction by either a slit or hair?
Something to think about…
The Fraunhofer diffraction patterns are a spectrum of the light passing
through the object and relate to a very powerful area of mathematics called
Fourier Analysis.
The central part of the Fraunhofer diffraction pattern contains information
about the larger structures in your slide. The dots further out are the
information about smaller structures on the slide.
Figure 4.12 Fraunhofer diffraction patterns of a grid and vertical slit
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