1) In a solution, many billions of molecules are in the path of the light beam and at
any given moment these molecules are present in all possible directions.
2) If the beam of plane-polarized light passes through a solution of an achiral
compound:
i) The effect of the first encounter might be to produce a very slight rotation of
the plane of polarization to the right.
ii) The beam should encounter at least one molecule that is in exactly the mirror
image orientation of the first before it emereges from the solution.
iii) The effect of the second encounter is to produce an equal and opposite rotation
of the plane ⇒ cancels the first rotation.
iv) Because so many molecules are present, it is statistically certain that for each
encounter with a particular orientation there will be an encounter with a
molecule that is in a mirror-image orientatio ⇒ optically inactive.Figure 5.13 A beam of plane-polarized light encountering a molecule of 2-propanol
(an achiral molecule) in orientation (a) and then a second molecule in
the mirror-image orientation (b) The beam emerges from these two
encounters with no net rotation of its plane of polarization.
3) If the beam of plane-polarized light passes through a solution of a chiral
compound:
i) No molecule is present that can ever be exactly oriented as a mirror image of
any given orientation of another molecule ⇒ optically active.