Gregory, James

The correct answer is (c). Refracting telescopes use lenses to bend light, and this bending can cause different colors of light to focus at slightly different points, resulting in a blurry image.

The correct answer is (b). A concave mirror curves inward, allowing it to gather and focus light effectively.

The correct answer is (c). The level of precision needed to create the mirrors for a reflecting telescope was beyond the capabilities of the time.

The correct answer is (b). Isaac Newton, inspired by Gregory's work, built the first successful reflecting telescope in 1668.

The correct answer is (a). Gregory was a pioneer in calculus, making contributions to the theory of infinite series, and he developed important theorems in geometry.

Here is a sample answer:

Diagram: A basic sketch would show a large concave primary mirror at the back of the telescope tube, a smaller secondary mirror positioned near the front, reflecting the light towards the side of the tube where the eyepiece is located.

Challenges:

• **Precision:** The most significant challenge would be achieving the required precision in grinding and polishing the mirrors. 17th-century technology was not advanced enough to create perfectly smooth and parabolic surfaces.
• **Materials:** Finding suitable materials for the mirrors would be another obstacle. Glass was available, but it was often flawed and difficult to work with.
• **Supporting structure:** Building a sturdy and stable structure to support the mirrors would be essential to prevent vibrations and maintain alignment. This was also technologically demanding.

Materials:

• **Mirrors:** The ideal choice would be a large, thick piece of polished glass. Metal mirrors were also used in the early days, but they were prone to tarnishing.
• **Tube:** Wood or metal could be used for the telescope tube, as long as it was rigid and stable.
• **Eyepiece:** Simple lenses could be used for the eyepiece, but they would likely have a limited field of view and suffer from some chromatic aberration.

Grinding and Polishing:

• **Grinding:** The mirrors would be ground by hand using rough abrasives like sand or emery. This process would take weeks or even months to achieve a rough shape.
• **Polishing:** Finer abrasives like polishing powders and cloth would then be used to polish the surface, gradually smoothing it out. This would also be a time-consuming and painstaking process.

Important Note: Even with the best tools and materials, it is unlikely a 17th-century scientist could have built a truly high-quality reflecting telescope. Newton's successful design relied on advancements in optics and precision engineering that were not yet available in Gregory's time. Gregory's true genius lay in his vision and theoretical understanding, even if the practical realization of his ideas had to wait for future generations.