Recall the definitions

• Optical isomerism arises due to chirality. The isomers are non-superimposable mirror images of each other.
• Geometrical isomerism arises due to restricted rotation (typically around a double bond or in cyclic compounds), giving cis-trans / E-Z forms.

Identify the common feature

Both optical and geometrical isomerism involve compounds having the same molecular formula and same connectivity of atoms, but differing in the spatial arrangement of atoms.

Such isomerism is called stereoisomerism.

Evaluate each option

Option A: "each forms equal number of isomers for a given compound"

• This is not generally true.
• Optical isomerism may give 2 enantiomers, sometimes more in molecules with multiple chiral centers.
• Geometrical isomerism may give 2 isomers in simple cases, but not always equal in all compounds.
• So, A is false.

Option B: "if in a compound one is present then so is the other"

• A compound may show optical isomerism without geometrical isomerism, and vice versa.
• Example: lactic acid shows optical isomerism but not geometrical isomerism.
• 2-butene shows geometrical isomerism but not optical isomerism.
• So, B is false.

Option C: "both are included in stereoisomerism"

• This is exactly correct.
• Both optical and geometrical isomerism are types of stereoisomerism.
• So, C is true.

Option D: "they have no similarity"

• False, because both belong to stereoisomerism.

Conclusion

The correct answer is: $\boxed{\text{C}}$

Comparison with stored correct answer

Stored correct answer = C

My derived answer = C

Hence, they agree.