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

To determine if the telescope with a diameter of 0.21 m is suitable for observing a crater of diameter 1 km on Pluto, we can use the formula for angular resolution:

ext{Resolution} = 1.22 rac{ ext{wavelength}}{ ext{diameter}}

Plugging in the values:

• Wavelength = 450 nm = $4.5 \times 10^{-7}$ m
• Diameter = 0.21 m

We find: $ext{Resolution} = 1.22 \frac{4.5 \times 10^{-7}}{0.21} \approx 2.62 \times 10^{-6} \text{ radians}$

To convert the angular resolution to a linear measurement on Pluto:

• Distance to Pluto = 12 500 km = $1.25 \times 10^{7}$ m
• Size of the crater = Diameter of crater = 1 km = 1000 m

Using the relationship: $\text{Diameter in view} \approx \text{Resolution} * ext{Distance}$, we find: $ext{Diameter in view} = 2.62 \times 10^{-6} \times 1.25 \times 10^{7} \approx 32.75 \text{ m}$

Since 32.75 m is much larger than 1 km, the telescope will not be suitable for observing such a small feature.

The collecting power of a telescope is proportional to the area of its aperture. The area can be calculated using:

$A = \pi \left(\frac{D}{2}\right)^2$

For the Hubble telescope with a diameter of 2.4 m: $A_{Hubble} = \pi \left(\frac{2.4}{2}\right)^2 \approx 4.52 \text{ m}^2$

For the spacecraft telescope with a diameter of 0.21 m: $A_{Spacecraft} = \pi \left(\frac{0.21}{2}\right)^2 \approx 0.0345\text{ m}^2$

Comparing both: $\text{Ratio} = \frac{A_{Hubble}}{A_{Spacecraft}} \approx \frac{4.52}{0.0345} \approx 131.5$

This shows that the Hubble has significantly greater collecting power than the spacecraft telescope.

In deciding between a reflecting telescope and a refracting telescope for the spacecraft, we must consider various factors:

1. Aberrations: Reflecting telescopes are less susceptible to chromatic aberration, which occurs in refractors due to differing wavelengths bending at different angles. Given the operational environment and the need for high-resolution images, a reflecting telescope is often more preferable.

2. Size and Weight: Reflectors can be constructed larger than refractors without the same weight constraints. This is pivotal in a spacecraft scenario where weight is critical.

3. Maintenance: Reflectors require less maintenance compared to refractors, especially when considering potential adjustments necessary in the lenses of refractive systems due to environmental factors.

Considering these factors, and with the capability to capture clearer images in diverse wavelengths, a reflecting telescope would be the more suitable choice for the spacecraft.