A sugar solution in a tube of length 2.0 dm produces optical rotation of 12°. Then, the sugar solution to one half of its initial concentration. If the dilute solute solution is contained in another tube of length 3.0 dm, the optical rotation produced by it will be:

Concept:

• A polarizer is a device through which only light waves oscillating in a single plane may pass.
• A polarimeter is an instrument used to determine the angle through which plane-polarized light has been rotated by a given sample.
• The optical rotation is the angle through which the plane of polarization is rotated when polarized light passes through a layer of a liquid.
• Substances are described as dextrorotatory or levorotatory according to whether the plane of polarization is rotated clockwise or counterclockwise, respectively, as determined by viewing towards the light source. Dextrorotation is designated (+) and levorotation is designated (-).
• The specific rotation is a characteristic property of a certain substance and is the standard measurement for the optical rotation of that substance.

The optical rotation and specific rotation are related by 

\([ α ] = \frac {α_{observed}}{c \times l}\)

where [α] is specific rotation and α_observed is optical rotation, c is the concentration (g/dl) and l is path length (dm);

Calculation:

Given α_observed = 12° when l = 2 dm and concentration c;

\( [ α ] = \frac {12}{c \times 2} = \frac {6}{c}\)

Now the concentration is c/2 and l = 3 dm

\( \frac {6}{c}=\frac {α_{observed}}{{\frac {c}{2}}\times 3}\)

α_observed = 9°