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Explain what is meant by the Rayleigh criterion - AQA - A-Level Physics - Question 5 - 2021 - Paper 4
Question 5
Explain what is meant by the Rayleigh criterion. The Rayleigh criterion defines the minimum angular separation at which two objects can be distinctly resolved. Spec... show full transcript
Worked Solution & Example Answer:Explain what is meant by the Rayleigh criterion - AQA - A-Level Physics - Question 5 - 2021 - Paper 4
Step 1
Explain what is meant by the Rayleigh criterion.
Answer
The Rayleigh criterion is a principle in optics that specifies the resolution limit of optical systems. It identifies the smallest angular separation that can be resolved between two point sources of light. When the diffraction pattern of two sources overlaps significantly, the ability to distinguish them as separate entities diminishes. Mathematically, it can be described by the formula:
where ( \theta ) is the minimum angle of resolution, ( \lambda ) is the wavelength of light, and ( D ) is the diameter of the aperture. This criterion is crucial in determining the capabilities of telescopes and microscopes.
Step 2
Explain why this telescope must be located in space.
Answer
The telescope operates within the wavelength range of 90 nm to 120 nm, which is part of the ultraviolet spectrum. Earth's atmosphere absorbs most ultraviolet radiation, preventing such wavelengths from reaching ground-based instruments. Therefore, to effectively observe these wavelengths, the telescope must be deployed in space, where it can avoid atmospheric absorption and interference.
Step 3
Discuss one advantage this telescope has compared to a telescope with the same aperture that uses visible light.
Answer
One significant advantage of using ultraviolet wavelengths is that they allow for the detection of phenomena that are not visible in the optical spectrum. For instance, UV observations can reveal more about hot stars and the formation of new stars, which emit more strongly at these wavelengths compared to visible light. This results in richer and more detailed data about high-energy processes in the universe.
Step 4
Compare the performances of the telescopes in Table 1 when both are used to detect the same faint radio objects.
Answer
When comparing the Arecibo and Lovell telescopes, one can assess their performance based on their collecting power and detail resolution.
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Collecting Power: The larger diameter of the Arecibo telescope (305 m) allows it to collect significantly more radio waves compared to the Lovell telescope (76 m). This greater collecting area results in improved signal strength from faint radio objects, allowing for better observational capability. It can be calculated that the Arecibo telescope collects approximately:
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Resolution: In terms of resolution, though both telescopes can detect radio waves at 21 cm, the Arecibo's larger diameter also generally leads to better angular resolution, which is beneficial for distinguishing closely spaced objects. The Lovell telescope, with its parabolic dish shape, also performs well but may not match the Arecibo's clarity due to its smaller size.