AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Relation between brightness and apparent magnitude. Difference of 1 on…
Full specification wording
Classification by luminosity (A-level only): Relation between brightness and apparent magnitude. Difference of 1 on magnitude scale is equal to an intensity ratio of 2.51.
Apparent magnitude m is a logarithmic measure of how bright a star appears from Earth.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 4 of 5
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Apparent magnitude m is a logarithmic measure of how bright a star appears from Earth. A difference of 1 magnitude corresponds to an intensity ratio of about 2.51, because 2.51 is the fifth root of 100. The scale runs backwards: smaller or more negative m means brighter. For two stars, m₂ − m₁ = 2.5 log₁₀(I₁/I₂), where I is received intensity. For example, if m₁ = 1 and m₂ = 6, the difference is 5. Using the formula, 5 = 2.5 log₁₀(I₁/I₂), which simplifies to log₁₀(I₁/I₂) = 2, so I₁/I₂ = 100. This means the first star appears 100 times brighter than the second. Conversely, a negative difference (m₂ − m₁ < 0) means the second star is brighter.
What earns the marks
- Apparent magnitude is a logarithmic scale of observed brightness, with smaller or more negative values indicating brighter objects.
- Use the relation m₂ − m₁ = 2.5 log₁₀(I₁/I₂) correctly, identifying which star is brighter.
- A magnitude difference of 1 corresponds to an intensity ratio of 2.51 because 2.51⁵ ≈ 100.
- Calculate an intensity ratio from a magnitude difference using powers of 2.51, or find a magnitude difference from an intensity ratio using logarithms.
- Interpret a negative magnitude difference (m₂ − m₁ < 0) as the second star being brighter than the first, since m₂ < m₁.
Common mistakes and how to put them right
Treating a larger magnitude as brighter.
Put it right by stating that smaller or more negative magnitudes correspond to greater brightness.
Using a ratio of 2.5 instead of 2.51 for a one-magnitude difference.
Put it right by using 2.51, the fifth root of 100.
Reversing the intensity ratio in the logarithmic equation.
Put it right: Ensure the brighter star (smaller magnitude) has the larger intensity in the ratio.
Exam tips
- Write the magnitude equation before substituting values so the examiner can see your method.
- When a magnitude difference is a multiple of 5, use the fact that 2.51⁵ ≈ 100 to simplify the calculation.
Try the lesson
The start of the Classification by luminosity (A-level only): Relation between brightness and apparent magnitude. Difference of 1 on magnitude scale is equal to an intensity ratio of 2.51. lesson, made from checked teaching notes for this specification point.
Have a go first
A star has apparent magnitude 4. A second star has apparent magnitude 5. According to the magnitude scale, the star of magnitude 4 is how many times brighter in intensity than the star of magnitude 5?
Listen
Apparent magnitude m is a logarithmic measure of how bright a star appears from Earth. A difference of 1 magnitude corresponds to an intensity ratio of about 2.51, because 2.51 is the fifth root of 100. The scale runs backwards: smaller or more negative m means brighter. For two stars, m₂ − m₁ = 2.5 log₁₀(I₁/I₂), where I is received intensity. For example, if m₁ = 1 and m₂ = 6, the difference is 5. Using the formula, 5 = 2.5 log₁₀(I₁/I₂), which simplifies to log₁₀(I₁/I₂) = 2, so I₁/I₂ = 100. This means the first star appears 100 times brighter than the second. Conversely, a negative difference (m₂ − m₁ < 0) means the second star is brighter. A strong answer earns marks for these points. Apparent magnitude is a logarithmic scale of observed brightness, with smaller or more negative values indicating brighter objects. Use the relation m₂ − m₁ = 2.5 log₁₀(I₁/I₂) correctly, identifying which star is brighter. A magnitude difference of 1 corresponds to an intensity ratio of 2.51 because 2.51⁵ ≈ 100. Calculate an intensity ratio from a magnitude difference using powers of 2.51, or find a magnitude difference from an intensity ratio using logarithms. A common slip: Treating a larger magnitude as brighter. Instead, stating that smaller or more negative magnitudes correspond to greater brightness. Exam tip: Write the magnitude equation before substituting values so the examiner can see your method.
Key words
Say what each word means before you turn the card.
Apparent magnitude
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Intensity ratio
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Magnitude difference
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See every definition
- Apparent magnitude
- A logarithmic measure of how bright a star appears from Earth, where smaller or more negative values indicate brighter objects.
- Intensity ratio
- The ratio of received intensities of two stars, related to their magnitude difference by m₂ − m₁ = 2.5 log₁₀(I₁/I₂).
- Magnitude difference
- A difference of 1 on the magnitude scale is equal to an intensity ratio of 2.51, because 2.51 is the fifth root of 100.
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