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# HW1-6130 - Homework I Size Measurement Size...

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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 four-sided and a six-sided 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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