Measurement of Length

For measuring large distances, parallax method is used

Parallax is an apparent displacement of an object viewed along two different lines of sight.

If we hold a pencil such that it covers a spot on the wall when our left eye is closed, and then open the left eye and close the right, parallax can be observed.

The distance between the two points of observation is called basis.

If we observe a planet S at a distance D from earth, from two points A and B which are d distance apart on earth, then, angle inscribed by AB on the planet, angle ASB is called parallax angle or parallactic angle. Here, we take AB as an arc of the circle with centre S and radius D.
So, D=b/angle ASB (if angle ASB is taken in radians). Thus we get D. (basis/angle)

Similarly, we can determine the diameter of the planet. If d is the diameter, and dAd' the angular size (angle subtended by d at earth),
then dAd' = d/D (diameter / distance)

For estimation of very small distances:we will have to use special methods.

An optical microscope can view objects of size greater than its wavelegth (4000 Å to 7000 Å) 1 angstrom = 1.0 × 10^-10 meters.

For smaller wavelengths, electron beams are used (electron micrsoscope). But due to the wave behaviour of electrons even this method has limitations. The maximum resolution of electron microscope is upto 0.6 Å.

Tuunneling microscopy is being developed which can go to even smaller scales.

But, the size of molecules can be estimated.

Oleic acid is a soapy liquid with a large molecular size.

1. 1 cu.cm of oelic acid is dissolved in alcohol to get 20 cu.cm solution.
2. 1 cu.cm of this solution is taken and diluted to 20 cu.cm using alcohol
   Now, the concentration of the solution is 1/400 cu.cm of oelic acid per cu.cm
3. some lycopodium powder is sprinkled on surface of water in a large trough
4. one drop of this solution is put in the water
   the oelic acid drop spreads into a thin, large, circular film of molecular thickness
5. The diameter of the film is measured to get its area.
6. The volume of the amount of drops we've put is determined.
   Let that be n cu.cm
7. The amount of oelic acid in this solution is
   n/400 cu.cm
8. The oelic acid forms a thin layer of thickness t
   this t = volume of the film/area of the film
   ie t = n / (400 * area ) cm
9. if the film is of mono-molecular thickness, then this becomes the diameter of oelic acid molecule.
   

Next: Range and Order of Lengths
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