# The Sun’s luminosity

##### Demonstration

Students collect data and gain experience in using the inverse-square law for intensity of radiation. They use simple but ingenious apparatus to deduce a value that cannot be measured directly.

#### Apparatus and materials

Lamp, 240 V 150 W or 100 W

Mains extension cable fed through earth-leakage circuit-breaker (ELCB)

A4 paper, plain white, one sheet

Optical pin or similar pointed object (e.g. drawing compass)

Cooking oil, a few ml, in a small beaker or cup

Tape measure or metre ruler

#### Health & Safety and Technical notes

Make sure that participants do not look directly at the Sun. Ensure that the extension cable is safely positioned so as not to trip up passers-by, and that connections to the lamp and power supply are protected from moisture. Check that the ELCB is operating (by using its Test button) before use.

The lamp should ideally be clear glass and held in a standard batten holder.

#### Procedure

This activity needs to be performed outdoors on a clear sunny day.

a Use the pin to place a very small drop of oil on the paper – it should spread to form a translucent patch no more than 5 mm diameter and ideally smaller.

b Hold the paper so that it is illuminated by the Sun on one side and by the lamp on the other, as shown in the diagram.

c Viewing the paper from the ‘Sun side’, adjust its distance from the lamp so that the oil spot appears to merge with the surrounding paper.

d Record the lamp distance d.

e Assume that the light from the lamp and from the Sun varies in intensity according to an inverse-square law, and using the Earth-Sun distance of 1.50 x 1011 m, obtain a value for the Sun’s luminosity, Lsun.

f Discuss factors that might affect the result.

#### Teaching notes

1 This activity can be carried out in a few minutes as a quick demonstration, followed by calculation and discussion.

Alternatively, the demonstration could be followed by setting a challenge to students: how can they design their own experimental set-up so as to reduce uncertainties in measurement?

2 When the spot appears to merge into the surrounding paper, the intensity of illumination due to the lamp (seen through the translucent spot) is the same as that due to the Sun on the surrounding paper.

With D the Earth-Sun distance, d the lamp distance and Llamp the luminosity (power) of the lamp (150 W or 100 W):

Lsun/(4πD2) =Llamp/(4πd2)

which can be rearranged to obtain a value for Lsun.

The calculated value generally lies within an order of magnitude of the accepted value for the Sun’s luminosity: Lsun = 3.9 x 1026 W.

3 In addition to uncertainties in judging and measuring the correct position of the paper, the result is affected by two sources of systematic error.

• Solar radiation that reaches the Earth’s surface is absorbed by the atmosphere. The amount of absorption depends on the elevation of the Sun above the horizon, and atmospheric conditions. Near midday in the UK in summer, on a clear day, about 30% of the radiation may be absorbed.
• The judgement of the correct position for the paper depends on sampling only the fraction of radiation to which human eyes are sensitive. As the Sun and the lamp have very different temperatures, they do not emit the same fraction of visible radiation.

This experiment comes from Salters Horners Advanced Physics© University of York Science Education Group.

Diagrams are reproduced by permission of the copyright holders, Heinemann.