Stereoisomers are those isomers that have the same molecular formula and chemical bonds but they have different spatial arrangements of atoms. As already mentioned, stereoisomerism involves two types of isomerism viz., geometrical isomerism and optical isomerism. These are discussed below:

1. Geometrical isomerism

Geometrical isomerism arises in heteroleptic complexes due to ligands occupying different positions around the central ion. The ligands occupy positions either adjacent to one another or opposite to one another. These are referred to as cis-form (ligands occupy adjacent positions) and trans- form (ligands occupy opposite positions). This type of isomerism is, therefore, also referred to as cis-trans isomerism. This type of isomerism is very common in coordination compounds. This is due to different coordination numbers varying from 2 to 9, commonly encountered in these compounds.

2. Optical isomerism

There are certain substances that can rotate the plane of polarised light. These are called optically active substances. The isomers which rotate the plane of polarised light equally but in opposite directions are called optically active isomers. These are also called enantiomers or enantiomorphs. The isomer which rotates the plane of polarised light to the right is called dextro rotatory designated as (d) and the one which rotates the plane of polarized light to the left is called laevo rotatory designated as (l). A 1 : 1 equilibrium mixture of d and l isomers gives a net zero rotation and is also called racemic mixture. The d and l isomers are mirror images of each other just as left hand is mirror image of the right hand. These mirror image compounds are non-superimposable on each other and do not possess the plane of symmetry. These optical isomers also possess the property of chirality (handedness). The essential condition for a substance to show optical activity is that the substance should not have a plane of symmetry in its structure. The optical isomers have identical physical and chemical properties. They differ only in the direction in which they rotate the plane of polarised light

A similarity between optical and geometrical isomerism is that

both are included in the stereoisomerism

The correct answer is option 3. both are included in the stereoisomerism.

The similarity between optical and geometrical isomerism is that both are included in stereoisomerism.

Here is a brief explanation of each option:

1. each gives an equal number of isomers for a given compound 

This statement is incorrect because optical and geometrical isomers do not necessarily yield an equal number of isomers. The number of each type of isomer depends on the specific structure and symmetry of the molecule.

2. if in a compound one is present, then so is the other

This statement is incorrect because optical isomerism and geometrical isomerism are distinct types of isomerism that do not always coexist in the same compound. A compound may have optical isomers, geometrical isomers, both, or neither, depending on its molecular structure.

3. both are included in the stereoisomerism

This statement is correct. Stereoisomerism is a broader category that encompasses both optical isomerism (where isomers are non-superimposable mirror images) and geometrical isomerism (where isomers differ in spatial arrangement around a double bond or ring). Therefore, both optical and geometrical isomerism fall under the category of stereoisomerism.

4. they have no similarity

This statement is incorrect because optical and geometrical isomerism do share similarities, particularly in that they both involve different spatial arrangements of atoms or groups around a central atom, which results in isomers that differ in their spatial orientation but have the same connectivity.

Thus, the correct answer is: both are included in the stereoisomerism.