Experimental - Spectroscopy

www.spectroscopyonline.com June 2011 Spectroscopy 26(6) 21
a quantity that has magnitude and
direction. Vector functions can be
easily expressed using unit vectors,
which are vectors of length 1
along each dimension of the space
involved. It is customary to use
the representations i, j, and k to
represent the unit vectors in the x,
y, and z dimensions, respectively
(Figure 12). Vectors are typically
represented in print as boldfaced
letters. Any random vector can be
expressed as, or decomposed into,
a certain number of i vectors, j
vectors, and k vectors as is demonstrated
in Figure 12. A vector
function might be as simple as
F = xi + yj [7]
in two dimensions, which is illustrated
in Figure 13 for a few
discrete points. Although only a
few discrete points are shown in
Figure 13, understand that the vector
function is continuous. That is,
it has a value at every point in the
graph.
One of the functions of a vector
that we will have to evaluate is
called a dot product. The dot product
between two vectors a and b is
represented and defined as
a∙b = |a||b|cosϴ [8]
Thus, if the two vectors are
parallel (ϴ = 0° so cosϴ = 1) the
work is maximized, but if the two
vectors are perpendicular to each
other (ϴ = 90° so cosϴ = 0), the
object does not move and no work
is done (Figure 15).
. . . But We’ll Have to Wait
I hope you’ve followed so far —
but so far, it’s been easy. To truly
understand Maxwell’s first equation,
we need to do a bit more advanced
stuff. Don’t worry — our
job in “The Baseline” is to talk
you through it. Unfortunately,
we’re going to have to wait
until the next installment to
pursue the more advanced stuff
and get to the heart of Maxwell’s
first equation.
For more information on this topic, please visit:
www.spectroscopyonline.com/ball
UV/Vis and NIR Fiber Optic
Probes for Process and
Laboratory applications
David W. Ball is
normally a professor of
chemistry at Cleveland
State University in Ohio.
For a while, though, things
will not be normal: starting
in July 2011 and for the
commencing academic
year, David will be serving as Distinguished
Visiting Professor at the United States Air
Force Academy in Colorado Springs, Colorado,
where he will be teaching chemistry to
Air Force cadets. He still, however, has two
books on spectroscopy available through
SPIE Press, and just recently published two
new textbooks with Flat World Knowledge.
Despite his relocation, he still can be contacted
at d.ball@csuohio.edu. And finally,
while at USAFA he will still be working on
this series, destined to become another
book at an SPIE Press web page near you.
where |a| represents the magnitude
(that is, length) of a, |b| is the magnitude
of b, and cosϴ is the cosine
of the angle between the two vectors.
The dot product is sometimes
called the scalar product because
the value is a scalar, not a vector.
The dot product can be thought of
physically as how much one vector
contributes to the direction of the
other vector, as shown in Figure
14. A fundamental definition that
uses the dot product is that for
work, w, which is defined in terms
of the force vector F and the displacement
vector of a moving object,
s, and the angle between these
two vectors:
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w = F∙s = |F||s|cosϴ [9]
Transmission Reflection ATR Fluorescence Transflection