levo

Space

Luminosity, intensity and the inverse square law

  • 2 things to know
  • Papers 2 and 3

Overview

Recall questions on the difference between luminosity and received intensity, the equation linking them, why 4πd² appears, and the assumptions the equation makes.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Numbers

What are the luminosity of a star and the intensity received from it, and what equation relates them?

Numbers

Why does the distance appear as 4πd² in the intensity relationship, and what happens to the intensity if the distance is trebled?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is meant by the luminosity of a star?

    Model answer

    It is the total radiant power the star emits in all directions, measured in watts.

  2. 2

    What is meant by the radiation intensity received from a star?

    Model answer

    It is the radiant power arriving per unit area at the detector, measured in W m⁻².

  3. 3

    State the equation relating the intensity received from a star to its luminosity and distance:

    Model answer

    The equation is I = L/(4πd²), where d is the distance from the source.

  4. 4

    Why does the distance appear as 4πd² in this relationship?

    Model answer

    The emitted power spreads out uniformly over the surface of a sphere of radius d, and that sphere has area 4πd².

  5. 5

    What happens to the intensity received from a star if its distance from us were three times greater?

    Model answer

    The intensity would fall to one ninth of its value, because intensity is inversely proportional to the square of the distance.

  6. 6

    A star of luminosity 3.9 × 10²⁶ W is 1.5 × 10¹¹ m away. What intensity is received?

    Model answer

    I = 3.9 × 10²⁶/(4π × (1.5 × 10¹¹)²) = 1.4 × 10³ W m⁻².

Other ways to work this

The same content, four other ways.

What is inside Levo

Six ways to work the same material.

1Closed book
2Open book
3Closed book

The 3-step method, run for you

Answer cold, learn it, then prove it stuck. Levo tracks the jump between your first attempt and your last.

Working as a Physicist
Mechanics
Electric Circuits
Materials

Cram a whole paper in one sitting

Sort every topic into what you know and what you do not, then drill only the weak ones.

The gradient gives the .
accelerationvelocitydisplacement

Blank Blitz makes facts automatic

Rapid timed gap-fills on the terms and numbers you need to recall without thinking.

AThe equation is s = (u + v)t/2.
BThe equation is v = u + at.
CThe equation is s = ut + ½at².

Build It gets the exam shape right

Assemble a full-mark answer from its marking points, in the order an examiner wants them.

Speed means rate of change of distance.
TrueFalse

Test It catches misconceptions

Spot the fault in a statement. The traps are the mistakes students actually make.

721941163128510

Brain Breaks between sessions

Short focus games to reset attention, so the next set lands better than the last.

Every question in Space, on a schedule.

Attempt a question from memory, write the correct version, then attempt it again. Levo records the jump between your first attempt and your last, and brings each question back on the day you are due to forget it.

Or £46 a year, about £3.83 a month. Cancel anytime.