Which of the following is not a natural fibre? 

Polyester 

The correct answer is option 3. Polyester.

Polyester is a synthetic fiber, meaning it is man-made rather than occurring naturally. It is produced through chemical processes using polymers derived from petroleum-based products. Here's a brief explanation of each of the mentioned fibers:

1. Silk:  Silk is a natural fiber produced by silkworms during the process of creating their cocoons. The fibers are extracted from the cocoons and then woven into fabric. Silk is known for its smooth texture and lustrous appearance.

2. Cotton:  Cotton is a natural fiber obtained from the seed hairs of the cotton plant. Cotton fibers are widely used in textile production, and the material is valued for its breathability, absorbency, and comfort.

3. Polyester: Polyester is a synthetic fiber made from chemical reactions involving polymers derived from petrochemicals. It is a versatile and durable material that is often used in various textiles, including clothing, upholstery, and bedding. Polyester is known for its resistance to wrinkles and shrinking.

4. Wool: Wool is a natural fiber obtained from the fleece of sheep and other animals like goats (cashmere and mohair), rabbits (angora), and alpacas. Wool fibers are known for their insulation properties, moisture-wicking ability, and natural elasticity.

In summary, while silk, cotton, and wool are natural fibers derived from animal or plant sources, polyester is a synthetic fiber manufactured through industrial processes involving chemicals and polymers.