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

To assess the suitability of the telescope:

1. Calculate the resolution of the telescope using the formula: $ext{Resolution} = 1.22 \frac{\lambda}{D}$ where (D) is the aperture diameter (0.21 m) and (\lambda) is the wavelength (450 nm or (450 \times 10^{-9} m)).
2. Substitute values: $\text{Resolution} = 1.22 \times \frac{450 \times 10^{-9}}{0.21} \approx 2.2 \times 10^{-7} m.$
3. This equates to a minimum resolvable detail on Pluto. Compare this to the 1 km diameter of the crater.
4. Comment that since the resolution of the telescope is much finer than the crater size, it is suitable for studying details on the surface.

To compare collecting powers:

1. The collecting power is proportional to the area of the aperture: $A = \pi \left( \frac{D}{2} \right)^2$
   • For the Hubble telescope (2.4 m diameter), $A_{Hubble} = \pi \left( \frac{2.4}{2} \right)^2 \approx 4.52 m^2.$
   • For the spacecraft telescope (0.21 m diameter), $A_{spacecraft} = \pi \left( \frac{0.21}{2} \right)^2 \approx 0.0346 m^2.$
2. Calculate the ratio of collecting powers: $\text{Ratio} = \frac{A_{Hubble}}{A_{spacecraft}} \approx 130.$ This shows that the Hubble telescope has a significantly larger collecting power.

When deciding between a reflecting telescope and a refracting telescope:

1. Reflecting telescopes are favored for their ability to eliminate chromatic aberration and can support larger apertures without excess weight.
2. They also allow for shorter focal lengths and are easier to construct for large diameters, making them more suitable for astronomical observations.
3. Refracting telescopes can have chromatic aberration issues, which affects image clarity.
4. Justify that a reflecting telescope would generally be the better choice for observing distant celestial objects, like those observed on Pluto.