Which of the following will not show optical isomerism ?

Options

A. `Cl-CH=C=CH-Cl`
B. `Br-CH=C=CH-Br`
C.
D.

Explanation

To determine which of the given compounds does not show optical isomerism, we need to analyze each compound for the presence of a plane of symmetry. Optical isomerism occurs when a molecule can exist in two non-superimposable mirror images, which typically happens when there is no plane of symmetry in the molecule.

### Step-by-Step Solution:

1. **Understand Optical Isomerism**:
- Optical isomerism arises in compounds that lack a plane of symmetry. If a compound has a plane of symmetry, it cannot have optical isomers.

2. **Analyze Each Compound**:
- **Compound A**:
- Structure: C1=C2 (with Cl and H on C1 and C2).
- Analysis: If the two terminal carbons have different groups, this compound will show optical isomerism because it lacks a plane of symmetry.

- **Compound B**:
- Structure: C1=C2 (with Br and H on C1 and C2).
- Analysis: Similar to Compound A, if the two terminal carbons have different groups, this compound will also show optical isomerism due to the absence of a plane of symmetry.

- **Compound C**:
- Structure: Fischer projection with groups COOH, H, OH.
- Analysis: This compound has a plane of symmetry that divides it into two equal halves, making it optically inactive. Therefore, it does not show optical isomerism.

- **Compound D**:
- Structure: Newman projection converted to Fischer projection.
- Analysis: After conversion, if there are no identical groups on the same carbon and no plane of symmetry, this compound will show optical isomerism.

3. **Conclusion**:
- The only compound that does not show optical isomerism is **Compound C** due to the presence of a plane of symmetry.

### Final Answer:
The compound that will not show optical isomerism is **Compound C**.