2 - chlorobutane + Cl _ 2 → C _ 4 H _ 8 Cl _ 2 (isomers) Total...

Optical activity is the ability of a substance to rotate the plane of polarisation of a beam of light that is passed through it.A compound to be said as optically active is only if it has to have an asymmetric chiral carbon centre (the carbon is said to be chiral if they have different substituents attached).

The optically active substances that rotate the plane of polarisation of the light towards the right are known as right-handed or dextrorotatory. It can be Indicated by including (+) or ‘D’ before the compound name.

Substances that rotate the plane of polarisation of the light toward the left are known as left-handed or laevorotatory. It can be Indicated by including (-) or ‘L’ before the compound name

The reaction is as follows,

$2 - chlorobutane + {Cl}_{2} \to {C}_{4}{H}_{8}{Cl}_{2}$ 

 ${C}_{4}{H}_{8}{Cl}_{2}$ will give four isomers of which one is optically inactive. Their structures are as follows,

 

Here only two, i.e., II and IV are optically active. Since each optically active compound has two enantiomers, therefore, total $6$ isomeric compounds are possible.