Question

1. A)how would parallax effect a measurement

1. B) Give several instances when error can be introduced while making a measurement.

1.C) Elaborate on the statement that "all measurements have a degree of uncertainty".

Answer 1

1.A) Whenever we view an object (say some measurement on a device) from two different lines of sight, a parallax is introduced. For example, while measuring length using a ruler, if we look at the ruler from a position directly above, we will get some value for the length. But if we tilt our head a bit leftward or rightward, we may see a slightly different value. This is the parallax error. More the skewness in observation of measurement, more the parallax error introduced. Parallax plays an important effect role in optics, astronomy, photography, firearms shooting etc.

1.B) There are various kinds of errors that get introduced while making measurements:

a) There can be some fault in the measuring device itself. Such an error is known as systematic instrument error. For example, the starting measurement of a vernier caliper may not be 0.00 cm but say 0.02 cm or something. Or perhaps, the least value of a specific voltmeter may not be 0 V but 0.2 V. Then we have to accordingly calibrate our results manually (add or subtract).

b) Some measurements may be wrong due to wrong observation. For instance, error introduced by parallax. If I observe the reading on a device with a tilted head, I may introduce this systematic observational error. Thus, it is advised to take readings from a position directly above the device.

c) Theoretical errors are introduced when there is change in initial conditions for the model of the experiment. For example, while measuring 'g', we neglect air resistance. But it's actually there and, though slightly, does affect our result.

d) Random errors are caused by a sudden, drastic change in experimental conditions and attenuation of the devices. Such errors are either positive or negative. For instance, changes in humidity and/or temperature, fluctuation in voltage etc. can lead to random errors. These errors may be nullified by taking a large number of readings and averaging the results from all.

1.C) It's true that all measurements have some degree of uncertainty. We assume that all the measurements (at a gross, classical level) have a true value. But it is due to our inefficiency or the limitations of our measuring devices that we cannot get that true value. For example, an object will have a true length. But our proximity to that true value depends on how we measure the length. A vernier caliper gives more precise result than a ruler, a screw gauge gives more precise result than a vernier caliper. Due to such limitations, we define the uncertainty involved in that measurement which accounts for both the accuracy and precision of the measurement. A means that the true value of the resistance lies between 29.5 and 30.5 and that is out best estimate. We may never know the true resistance here, but we can set limits to the value. Narrower the limits, more accurate the result.