        SOLUTION TO EXERCISE 11

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Using a ruler, I measured the distance from the bridge of my nose to my
pupil to be 3 cm.  Then I held my thumb out, closed my left eye, and
lined up my thumb with a streetlamp about a block away.  Next, I opened my
left eye and closed my right eye, and noticed that my thumb appeared to have
shifted three finger widths to one side.  This means that the shift was about
six degrees, since one finger width is about two degrees.  The "parallactic
angle" is thus half this, or about three degrees.  Thus,

tan(3 deg) = (3 cm) / r ,  so  r = 57 cm.

In the formulation with radians, we use the full distance between my pupils,
rather than just half the distance.  That's twice 3 cm.  So,

6 deg = (2 * 3 cm)/r = 6/57.3 = 0.105 radians

r = (2 * 3 cm) / 0.105 = 57 cm

Using a meter stick, I measured the distance between my forehead and my
outstretched thumb to be 52 cm.  That means my parallax estimation has an
error of (57 - 52)/52 = 10% error.  Sources of random (measurement) error
include an inaccurate measurement of the distance between the bridge of
my nose and my pupil, and an inaccurate measurement of the angle that my
thumb shifted.  A source of systematic error is that my finger width may
not be two degrees.  Actually, I'm pleasantly surprised I achieved such
a low error, considering my relatively non-rigorous experimental procedures.

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