Draw a ray diagram for a Cassegrain telescope - AQA - A-Level Physics - Question 1 - 2020 - Paper 4

To evaluate if the telescope on the spacecraft is suitable for studying a crater of 1 km diameter on Pluto:

1. Calculate the resolution capability of the telescope using the formula: $Resolution = \frac{1.22 \cdot \lambda}{D}$ Where (\lambda) is the wavelength (450 nm) and (D) is the aperture diameter (0.21 m).
2. Substitute the values: $Resolution = \frac{1.22 \cdot 450 \times 10^{-9}}{0.21} \approx 2.14 \times 10^{-6} m$
3. Convert the resolution into kilometers, which is approximately 0.00000214 km or 2.14 meters.
4. The smallest detail the telescope can resolve is about 2.14 meters, which means it can effectively study features larger than this. Since 1 km is significantly larger than 2.14 meters, the telescope is suitable for observing the crater.

To compare the collecting power between the Hubble telescope and the spacecraft telescope:

1. Use the formula for collecting power, which is proportional to the area of the aperture: $A = \pi \left( \frac{D}{2} \right)^2$
2. For the Hubble telescope (diameter 2.4 m): $A_H = \pi \left( \frac{2.4}{2} \right)^2 \approx 4.52 m^2$
3. For the spacecraft telescope (diameter 0.21 m): $A_S = \pi \left( \frac{0.21}{2} \right)^2 \approx 0.0346 m^2$
4. Calculate the ratio of their collecting powers: $\text{Ratio} = \frac{A_H}{A_S} = \frac{4.52}{0.0346} \approx 130$
5. This indicates that the Hubble telescope has a collecting power about 130 times greater than the telescope on the spacecraft.

To decide between a reflecting or refracting telescope for the spacecraft:

1. Reflecting Telescopes are generally preferred for larger apertures, as they avoid chromatic aberration and can be built larger without significantly increasing weight.
2. Refracting Telescopes can be simpler for smaller apertures but suffer from chromatic aberration, which can distort images.
3. Given that the telescope must operate in space, where light scattering is less of a problem and higher precision is required, a reflecting telescope is more suitable. Its design will allow for clearer images without distortion, making it the better option for observing features on Pluto.