Give reason: Racemic mixture is optically inactive.

Hint: The optic activity of the compound is related to its ability to rotate the plane of the polarized passing through it. The racemic mixture consists of the equal amount of the two enantiomers, which are optically active.

Complete step by step answer:
Firstly, a racemic mixture consists of a chiral molecule, which has no plane of symmetry, such that the mirror image of its optical isomers is non-superimposable over each other. Thus, making them non-identical and forming a mixture of the two enantiomers. The enantiomers have a tendency to interact with the plane polarised light, causing a rotation of its plane. When the plane of the polarized light is rotated clockwise on passing through the isomer, it is called a dextrorotatory isomer, whereas when the plane is rotated anticlockwise by the isomer, it is called the levorotatory isomer. So, in the racemic mixture, due to the presence of the two enantiomers in equal amounts, that is the amount of rotation caused by the dextro-isomer in clockwise direction is equal to the amount of rotation caused by the levo-isomer in anti-clockwise direction. So, the net rotation in the compound is zero. And as the compound with zero rotation is optically inactive. Thus, we have the racemic mixture with an equal ratio of the two isomers to be optically inactive in nature.

Note: The two enantiomers individually are optically active, but being present in equal amounts in the compound. It makes the mixture as optically inactive. This process is known as the external compensation.