The Griffith Observatory in Los Angeles includes an astronomical refracting telescope (Griffith telescope) with an objective lens of diameter 305 mm and focal length 5.03 m - AQA - A-Level Physics - Question 1 - 2018 - Paper 4

Using the typical human eye's angular resolution: 3.2 × 10⁻⁴ rad. The formula relating the eyepiece focal length (f_e) can be derived as follows, using the relation: $M = \frac{\theta_{eye}}{\theta_{object}} = \frac{f_e}{f_t}$ Where (f_t) is the focal length of the telescope, which is given as 5.03 m. Substituting the angular resolutions: $M = \frac{3.2 \times 10^{-4}}{1.8 \times 10^{-6}} \approx 177.78$ Now solving for focal length: $f_e = M f_t = 177.78 \times 5.03 \approx 893.5 \text{ m}$

Given the diameter of Apophis is 325 m and its distance from Earth is 3.0 × 10⁶ km: Using the angular resolution from the previous question: $\theta = \frac{d}{D}$ Where:

• (d) is the size of Apophis (325 m),
• (D) is the distance to Apophis in meters (3.0 × 10⁶ km = 3.0 × 10^{9} m). Calculating the angular resolution: $\theta = \frac{325}{3.0 \times 10^{9}} \approx 1.08 \times 10^{-7} \text{ rad}$ Since the angular resolution of the telescope is 1.8 × 10⁻⁶ rad, which is larger than the resolution needed to view Apophis, the telescope is not suitable for detailed observation.