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Theme B — The Particulate Nature of Matter

B.1.13 Apparent Brightness and Luminosity — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 15 of 53 1 quiz

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B.1.13 Apparent Brightness and Luminosity — IB PHYSICS SL notes: Define luminosity and apparent brightness and use b = L/4πd² for light from stars.Luminosity L = the total power output of radiation emitted by a star in all directions across all wavelengths.It is measured in watts…

  • At the star's surface
  • Apparent brightness b
  • Two factors
  • Difference
  • Sun's brightness at Earth
  • What the symbols mean

Part 1 of 8Luminosity

Luminosity L
Luminosity L the total power output of radiation emitted by a star in all directions across all wavelengths.
  • It is measured in watts.
Intrinsic
  • Intrinsic luminosity does not depend on the distance of the observer.
Sun
  • L = 3.83 × 1026 W.
At the star's surface
  • At the star's surface luminosity tells us how bright the star is there.

Part 2 of 8Apparent brightness

1Apparent brightness b
Apparent brightness b the intensity of radiation received on Earth from a star.
  • It is measured in W m−2, normal to the incoming radiation.
2Two factors
  • Two factors how much light the star emits and how far away it is.
3Difference
  • Difference luminosity is the total power output, while apparent brightness is what is measured on Earth.
4Sun's brightness at Earth
  • Sun's brightness at Earth about 1.36 × 103 W m−2 at 1.50 × 1011 m.

Part 3 of 8Inverse square law

Spreading
  • Spreading light leaving a star spreads uniformly through a spherical shell.
Area
  • Area the sphere has surface area 4πd2, where d is the distance between the star and the Earth.
Equation
  • Equation b = L/(4πd2).
    What the symbols mean: b or F = apparent brightness (W m−2) · L = luminosity (W) · d = distance to the star (m)
  • b is the apparent brightness in W m−2.
  • L is the luminosity in W.
  • d is the distance in m.
Proportion
  • Proportion b ∝ 1/d2, so twice as far means the same power over four times the area and a quarter of the brightness.
  • Three times as far gives one ninth.
Other uses
  • Other uses any quantity falling by the square of the distance, such as ionising radiation, follows this law.

Part 4 of 8Assumptions

Uniform emission
  • Uniform emission the star radiates equally in all directions.
No absorption
  • No absorption no radiation is absorbed or scattered on the way; dust and gas can dim distant stars.
All wavelengths
  • All wavelengths b is measured over all wavelengths, so detector responses need corrections.
Magnitude scale
  • Magnitude scale it is logarithmic and is a different system from b.

Part 5 of 8Using the equation

Using the equation
Finding luminosity
  • L = 4πd2b.
Finding distance
  • Finding distance d = √(L/4πb), if L is known.
Standard candles
  • Standard candles objects of known luminosity, such as Cepheid variables and Type Ia supernovae, give distances to galaxies.
Stars of the same luminosity
  • Stars of the same luminosity the one with the greater brightness is closer.
Equal brightness
  • Equal brightness it does not mean equal luminosity.

Part 6 of 8Comparing stars

Comparing stars
Ratio
  • Ratio b1/b2 = (L1/L2)(d2/d1)2, which removes constants such as 4π.
Twice as far, eight times the luminosity
  • Twice as far, eight times the luminosity bA/bB = 8 × (1/2)2 = 2.
Faint star
  • Faint star a star that looks faint may be distant yet very luminous, which is why independent distances such as parallax are needed.

Part 7 of 8Useful data and units

1Light-year
  • 9.46 × 1015 m.
2Parsec
  • 3.09 × 1016 m.
3Proxima Centauri
  • Proxima Centauri luminosity about 0.0017 of the Sun's, at 4.0 × 1016 m.
4Link
  • Link the Stefan–Boltzmann law gives L from radius and temperature, so radii can be found from L and T.
5Method
  • Method write b = L/4πd2 first, decide the unknown and convert distances to metres.

Part 8 of 8More from the specification

1
Radiation pyrometry of incandescent solids
  • Radiation pyrometry of incandescent solids analyzing blackbody emission curves determines the absolute surface temperature and radiant luminosity of dense solids.
2
Luminosity
  • Luminosity total power radiated by a star, while apparent brightness is intensity received, equal to luminosity divided by 4 pi d squared
3
Stefan-Boltzmann law
  • Stefan-Boltzmann law luminosity equals sigma times area times temperature to the fourth power
4
Specific heat capacity
  • Specific heat capacity thermal energy change equals mass times capacity times temperature change, for water or copper
5
Latent heat
  • Latent heat energy during a change of state breaks bonds between particles without changing the temperature of the liquid or solid
6
Phase change
  • Change of matter from one state to another
7
Thermal conductivity
  • Material constant relating the rate of conduction to the temperature gradient and area
8
Internal energy
  • Total random kinetic and potential energy of all particles.
9
Potential energy
  • Energy stored by the configuration of a system.
10
Conduction
  • Transfer of thermal energy by lattice vibrations and free electrons
11
Molecule
  • Tiny particle of the fluid, too small to be seen.
12
Capacity
  • Charge a cell can supply, in A h or C.
13
Density
  • Mass per unit volume.
14
Solid
  • State with a fixed shape and a fixed volume.
15
Fusion
  • Joining of light nuclei into a heavier one.
16
Kinetic energy
  • K = ½mv2, energy of motion.
17
Thermal equilibrium
  • Constant temperature because energy is absorbed and lost at equal rates
18
Thermal
  • A convection current in the air.
19
Liquid
  • State with a fixed volume that takes the shape of its container.
20
Copper
  • Metal widely used for electrical wires.
21
Convection
  • Transfer of thermal energy by the movement of a heated fluid

Key terms

TermMeaning
LuminosityThe total power output of radiation emitted by a star
Apparent brightnessThe intensity of radiation received from a star, in W m−2
Inverse square lawIntensity decreases as the square of the distance from the source
Standard candleObject of known luminosity used to find distance
Light-yearDistance travelled by light in one year, 9.46 × 1015 m
ParallaxApparent shift of a nearby star used to measure its distance

Avoid these mistakes

1
Using apparent brightness as luminosity — luminosity is the total power emitted.
2
Using the distance in light-years in the equation — convert to metres.
3
Using d instead of d2 — brightness follows an inverse square law.
4
Thinking the brighter-looking star is more luminous — distance matters.
5
Forgetting the assumption of no absorption by dust — it may dim the star.

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