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A2 · Practice questions · Standard candles

Known brightness, measured distance.

Six original Cambridge-style questions on luminosity and radiant flux intensity, the inverse square law F = L / 4πd², and how a standard candle gives the distance to a galaxy.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
Keep these straight

Luminosity is emitted, flux is received.

01
Analysis
[2 marks]

Distinguish between the luminosity of a star and the radiant flux intensity measured at the Earth, giving the SI unit of each.

  • Luminosity is the total power the star radiates in all directions, measured in W. ✓
  • Radiant flux intensity is the radiant power passing through unit area at the observer, measured in W m⁻², and it falls with distance while the luminosity does not. ✓
02
Calculation
[2 marks]

The Sun has luminosity 3.8 × 10²⁶ W and is 1.5 × 10¹¹ m from the Earth. Calculate the radiant flux intensity of sunlight just above the Earth's atmosphere.

  • F = L / 4πd² = 3.8 × 10²⁶ / (4π × (1.5 × 10¹¹)²). ✓
  • F = 3.8 × 10²⁶ / 2.83 × 10²³ = 1.3 × 10³ W m⁻². ✓
03
Calculation
[3 marks]

A type Ia supernova has a peak luminosity of 5.0 × 10³⁶ W. Its peak radiant flux intensity at the Earth is measured as 2.0 × 10⁻¹⁶ W m⁻². Calculate the distance to the supernova in metres and in light-years. (1 light-year = 9.5 × 10¹⁵ m.)

  • d² = L / 4πF = 5.0 × 10³⁶ / (4π × 2.0 × 10⁻¹⁶) = 1.99 × 10⁴⁵ m². ✓
  • d = √(1.99 × 10⁴⁵) = 4.5 × 10²² m. ✓
  • d = 4.46 × 10²² / 9.5 × 10¹⁵ = 4.7 × 10⁶ light-years. ✓
04
Analysis
[3 marks]

Explain what is meant by a standard candle, and explain why a type Ia supernova can be used as one.

  • A standard candle is an astronomical object whose luminosity is known independently of its distance. ✓
  • A type Ia supernova occurs when a white dwarf in a binary system accretes matter until it reaches a fixed critical mass, so every such explosion releases almost the same energy and reaches almost the same peak luminosity. ✓
  • Measuring the peak radiant flux intensity then gives the distance from F = L / 4πd², and the events are bright enough to be seen in very distant galaxies. ✓
05
Calculation
[3 marks]

Two stars have the same luminosity. Star P is 40 light-years from the Earth and star Q is 200 light-years away. Calculate the ratio of the radiant flux intensity received from P to that received from Q, and state what this means for how bright the two stars appear.

  • For equal L, F ∝ 1 / d², so Fₚ / F€ = (d€ / dₚ)² = (200 / 40)². ✓
  • Ratio = 5² = 25. ✓
  • P appears 25 times brighter than Q even though the stars emit equally, because the same power is spread over a sphere of 25 times the area at Q's distance. ✓
06
Calculation
[4 marks]

A Cepheid variable in a nearby galaxy is found, from its pulsation period, to have a luminosity of 2.4 × 10³¹ W. Its measured radiant flux intensity is 1.2 × 10⁻¹⁴ W m⁻².

(a) Calculate the distance to the galaxy. (b) A second Cepheid in the same galaxy has twice the luminosity of the first. Calculate the radiant flux intensity expected from it. (c) State one reason why Cepheids cannot be used to find the distance to the most distant galaxies.

  • (a) d = √(L / 4πF) = √(2.4 × 10³¹ / (4π × 1.2 × 10⁻¹⁴)) = √(1.59 × 10⁴⁴). ✓
  • d = 1.3 × 10²² m. ✓
  • (b) Same distance, double the luminosity, so F doubles: 2.4 × 10⁻¹⁴ W m⁻². ✓
  • (c) Individual Cepheids are far less luminous than a supernova, so beyond a few tens of millions of light-years their flux is too small to measure (or to resolve from the rest of the galaxy). ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.