Question 3

Two telescopes, $A\,$ and $B$ , are designed to study different regions of the electromagnetic spectrum:

Telescope $A\,$ is a ground-based infrared reflecting telescope with a primary mirror diameter $mD_A = 25.0\text{ m}$ , operating at an observing wavelength of $μm\lambda_A = 1.5\,\mu\text{m}$ .
Telescope $B\,$ is a single-dish radio telescope with a diameter of $mD_B = 125.0\text{ m}$ , operating at an observing wavelength of $mm\lambda_B = 7.5\text{ mm}$ .

Perform the following analyses:

Calculate the ratio of the collecting power of Telescope $B\,$ to Telescope $A$ .

Calculate the minimum angular resolution (using $θ≈λD\displaystyle \theta \approx \frac{\lambda}{D}$ ) for both telescopes, and determine which telescope can resolve finer spatial details.

Contrast their structural design and Earth-based positioning by stating one similarity in structure and one difference in their ideal positioning.