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The Kielder Observatory in Northumberland includes two optical telescopes attached to the same mount, so that they can be used to view the same object - AQA - A-Level Physics - Question 2 - 2017 - Paper 4
Question 2
The Kielder Observatory in Northumberland includes two optical telescopes attached to the same mount, so that they can be used to view the same object. Some of the p... show full transcript
Worked Solution & Example Answer:The Kielder Observatory in Northumberland includes two optical telescopes attached to the same mount, so that they can be used to view the same object - AQA - A-Level Physics - Question 2 - 2017 - Paper 4
Step 1
Suggest which telescope in Table 1 produces the brighter image. Support your answer with a suitable calculation.
Answer
To determine which telescope produces the brighter image, we analyze the collecting power of each telescope, which is related to the objective diameter. The collecting power is proportional to the area of the objective lens.
For Telescope A (Refractor): Area = π * (d/2)² = π * (70/2)² = π * 35² ≈ 3848.45 mm²
For Telescope B (Reflector): Area = π * (d/2)² = π * (400/2)² = π * 200² ≈ 125663.71 mm²
Since the area of Telescope B is significantly larger than that of Telescope A, Telescope B has a larger collecting power. Therefore, Telescope B produces a brighter image.
Step 2
Explain what is meant by the Rayleigh criterion.
Answer
The Rayleigh criterion defines the minimum angular resolution that a telescope can achieve, which is determined by the wavelength of light used and the diameter of the telescope's aperture. It states that two point sources are just resolvable when the central maximum of one diffraction pattern coincides with the first minimum of another. Mathematically, the criterion can be expressed as:
where:
- ( \theta ) = minimum angle of resolution in radians,
- ( \lambda ) = wavelength of light,
- ( D ) = diameter of the aperture.
Step 3
Discuss which of the two telescopes in Table 1 would be better at resolving the images of two objects that are close together.
Answer
Telescope B would be better at resolving the images of two objects that are close together. This is due to its larger diameter, which leads to a smaller minimum angular resolution according to the Rayleigh criterion. A larger aperture results in less diffraction and improved resolving power, allowing finer details to be distinguished between two closely spaced objects.