AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Λ Rayleigh criterion, θ ≈ D Collecting power is proportional to diameter .
Full specification wording
Advantages of large diameter telescopes (A-level only): λ Rayleigh criterion, θ ≈ D Collecting power is proportional to diameter .
The Rayleigh criterion gives the minimum angular resolution θ of a telescope as θ ≈ λ ÷ D, where λ is the wavelength of the radiation and D is the diameter of the objective aperture.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 2 of 4
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
The Rayleigh criterion gives the minimum angular resolution θ of a telescope as θ ≈ λ ÷ D, where λ is the wavelength of the radiation and D is the diameter of the objective aperture. The angle θ is in radians. Because the ratio is dimensionless, λ and D must simply be in the same units, not necessarily metres. A larger D produces a smaller θ, meaning finer detail can be resolved. Separately, the collecting power of a telescope is proportional to the area of its objective, so it is proportional to D². A larger diameter gathers more radiation per second, allowing fainter objects to be detected.
For example: Doubling D halves θ and quadruples the collecting power.
What earns the marks
- The Rayleigh criterion is θ ≈ λ ÷ D, with θ in radians, λ the wavelength and D the objective diameter.
- A smaller θ corresponds to better angular resolution, separating closer sources.
- Collecting power is proportional to the area of the objective, which is proportional to D².
- Doubling the diameter halves the minimum resolvable angle and increases collecting power by a factor of four.
Common mistakes and how to put them right
Writing collecting power as proportional to D rather than D².
Put it right: The objective is a circular area, so collecting power ∝ D².
Mixing units by substituting λ in nanometres while D is in metres.
Put it right: Convert both to the same unit so the ratio is dimensionless.
Confusing resolution with collecting power.
Put it right: Treat θ ≈ λ ÷ D as the resolution relationship and collecting power ∝ D² as the light-gathering relationship.
Exam tips
- Quote θ ≈ λ ÷ D and collecting power ∝ D² explicitly before using them.
- For comparison questions, calculate the ratio of diameters and use it to find both the change in θ and the change in collecting power.
Try the lesson
The start of the Advantages of large diameter telescopes (A-level only): λ Rayleigh criterion, θ ≈ D Collecting power is proportional to diameter . lesson, made from checked teaching notes for this specification point.
Have a go first
Which statement correctly describes how the collecting power of a telescope depends on its objective diameter D?
Listen
The Rayleigh criterion gives the minimum angular resolution θ of a telescope as θ ≈ λ ÷ D, where λ is the wavelength of the radiation and D is the diameter of the objective aperture. The angle θ is in radians. Because the ratio is dimensionless, λ and D must simply be in the same units, not necessarily metres. A larger D produces a smaller θ, meaning finer detail can be resolved. Separately, the collecting power of a telescope is proportional to the area of its objective, so it is proportional to D². A larger diameter gathers more radiation per second, allowing fainter objects to be detected. For example, doubling D halves θ and quadruples the collecting power. A strong answer earns marks for these points. The Rayleigh criterion is θ ≈ λ ÷ D, with θ in radians, λ the wavelength and D the objective diameter. A smaller θ corresponds to better angular resolution, separating closer sources. Collecting power is proportional to the area of the objective, which is proportional to D². Doubling the diameter halves the minimum resolvable angle and increases collecting power by a factor of four. Exam tip: Quote θ ≈ λ ÷ D and collecting power ∝ D² explicitly before using them.
See it
Key words
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Rayleigh criterion
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Collecting power
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Angular resolution
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See every definition
- Rayleigh criterion
- Gives the minimum angular resolution θ of a telescope as θ ≈ λ ÷ D, where λ is the wavelength and D is the diameter of the objective aperture.
- Collecting power
- Proportional to the area of the objective, so it is proportional to D², and a larger diameter gathers more radiation per second.
- Angular resolution
- Given by θ ≈ λ ÷ D in radians, and a larger D produces a smaller θ, meaning finer detail can be resolved.
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