Give two advantages that a telescope lens or mirror of large diameter has over one of small diameter
Two advantages of a telescope lens or mirror with a large diameter compared to one with a small diameter are increased light-gathering capability and increased resolution.
1. Increased Light-gathering Capability: The diameter of a telescope's lens or mirror determines its light-gathering capability. A larger diameter lens or mirror allows more light to enter the telescope, resulting in a brighter and clearer image. This is particularly important when observing faint objects in the sky, such as distant galaxies, nebulae, or dim stars. With a larger diameter, a telescope can capture more photons, enabling astronomers to see more details and gather more data.
To explain how to calculate the light-gathering capability, we use the formula for the area of a circle: A = π * r^2, where A is the area and r is the radius of the lens or mirror. As the radius (or diameter) increases, the area and, therefore, the amount of light collected by the telescope also increase.
2. Increased Resolution: The resolving power of a telescope is related to its diameter. Resolving power refers to the telescope's ability to distinguish fine details or separate closely-spaced objects. A larger diameter lens or mirror provides higher resolution, allowing us to see smaller and more precise features in celestial objects.
The resolution of a telescope is determined by the formula R ≈ λ/D, where R is the resolution, λ is the wavelength of light being observed, and D is the diameter of the lens or mirror. According to this formula, for a given wavelength of light, a larger diameter (D) results in a smaller resolution (R), meaning that finer details can be resolved.
By having a larger diameter, a telescope can collect more light and reveal faint objects, as well as provide higher resolution for clearer and more detailed observations.