Explanation:
Meso tartaric acid does not show optical activity because it has a plane of symmetry.

Optical Activity:
Optical activity refers to the ability of a compound to rotate the plane of polarized light. It occurs in substances that are chiral, meaning they are not superimposable on their mirror image.

Chirality:
Chirality is a property of a molecule that cannot be superimposed on its mirror image. Chiral molecules have a non-superimposable mirror image and contain at least one chiral center (also known as an asymmetric carbon atom).

Chiral Centers:
A chiral center is an atom in a molecule that is bonded to four different groups. This leads to the existence of two possible mirror images, known as enantiomers. Enantiomers are non-superimposable mirror images of each other.

Meso Compound:
A meso compound is a molecule that has chiral centers but is not chiral as a whole. It possesses a plane of symmetry, which divides the molecule into two identical halves. This results in the cancellation of the optical activity caused by the chiral centers.

Explanation of the Options:
a) It has two chiral centres: Having two chiral centers does not automatically make a compound chiral. In the case of meso tartaric acid, the presence of a plane of symmetry makes it meso and not chiral.

b) It shows external compensation: External compensation refers to the cancellation of optical activity due to the presence of equal amounts of two enantiomers. This is not the case with meso tartaric acid, as it does not have optical activity in the first place.

c) It has a plane of symmetry: This is the correct option. Meso tartaric acid possesses a plane of symmetry, which divides the molecule into two identical halves. This cancels out the optical activity caused by the chiral centers.

d) It has an erythro form: The erythro form refers to a specific stereochemical arrangement of substituents on a molecule. The presence of the erythro form does not determine the optical activity of a compound. In the case of meso tartaric acid, it is the presence of a plane of symmetry that causes it to be optically inactive.

Therefore, the correct answer is option 'C' - Meso tartaric acid does not show optical activity because it has a plane of symmetry.