Homework I: Size Measurement, Size Distribution (due January 21, 2009)
1.
Between what two circle numbers on the Porton graticule will the image of a
1
μ
m particle fall when viewed with a 43
×
objective and a 15
×
eyepiece?
Circle number 10 has an image diameter of 9.9 mm.
(10%)
2.
(a) A straight fiber has an aspect ratio of 5:1.
If the fiber is viewed
perpendicular to its axis, what is the maximum ratio of Feret’s diameter to
projected area diameter?
(b) For particles having a square projected cross
section, what is the ratio of Feret’s diameter (averaged over all orientations) to
the projected area diameter?
(12%)
3.
A particle has a smooth, circular cross section of diameter d
p
.
The fractal
dimension of the particle's perimeter is to be estimated by fitting a foursided
and a sixsided regular inscribed polygon to the circle.
Based only on this
information, what fractal dimension is estimated for this step size range.
[Hint:
The length b of the side of a regular inscribed polygon with n sides is b = d
p
×
sin(180
o
/n).] (15%)
4.
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 Spring '08
 Wu
 Standard Deviation, Mean, Ratio

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