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SOLUTION TO EXERCISE 11
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. |