PhysicsLAB: Illuminance by a Light Source

The purpose of this lab is to measure the properties of illuminance provided by a point source of light.

Illuminance is measured in lux (lx) and is a metric system unit that represents the ratio of lumens/m². This unit measures how the rays from a light source illuminate a surface placed at different distances form a point source. The unit of lumens measures luminous flux; that is, the "number" of light rays that pass through a surface which is at right angles to their direction of motion. This term has the same conations as magnetic flux and electric flux.

Suppose a light source emits 800 lumens. As the light rays move away from the source, they form light spheres. If one such light sphere had a total surface area of 800 m², then the illumination on one square meter would be 1 lux. If a different, smaller light sphere only has a surface area of 4.19 m², then the illuminance on one square meter would be 193.6 lux.

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As shown in the diagram above, illuminance is an inverse square property of light.

Equipment

optics bench (or a meter stick to measure distances)
point source of light
rigid, moveable screen
lens holder to secure light probe
computer with LoggerPro and appropriate interface for a light probe (measuring in lux)

shown: Pasco's Optics System OS-8515C
Vernier's Light Sensor

Procedure - Part I

Take a sheet of unlined paper and trace out the size of the moveable screen. Cut out the outline. Next draw two circles that are centered on the paper. Make one circle approximately 3-cm in diameter and the other approximately 15-cm in diameter. The actual size does not matter as long as the circles are drastically difference in diameter, are concentric, and fit completely on the paper.
Secure the paper to the front of the screen and mount the screen on the optics bench.
Turn on the light source (which has been placed at the "0" mark on the optics bench) and COMPLETELY DARKEN the room. Move the screen to a position where the beam from the light source completely fits the smaller circle. Record that position in the blank provided below. Then move the screen until the light beam completely fills the larger circle and record the second position in the blank provided below.

diameter of small circle (cm)

position on bench where the beam completely filled the small circle (cm)

diameter of larger circle (cm)

position on bench where the beam completely filled the larger circle (cm)

Procedure Part II

Leaving the light source in place remove the screen from the optics bench. Secure a light probe into the lens holder so that it does not move and its front surface is lined up with the lens holder's pointer that moves along the optic's bench.

Again, the room must be COMPLETELY DARKENED. Begin with the light probe (set to 0-6000 lux) 5 cm from the light source and read the lux value from the LoggerPro program. You do not need to graph the data, just observe the numerical data that is displayed on the lower left side of the screen. Once the reading stabilizes, record the value for 5 cm. Then move the lens holder back in 5-cm increments, recording the illuminance each time. As long as you can discriminate between readings, keep recording until you reach 100 cm.

Record your values in the chart below.

	probe position	illuminance
trial	(cm)	(lux)

Analysis

After collecting all of your data, you will now create two graphs in EXCEL. The first will be called Illuminance vs Distance and the second will be called Illuminance vs (1/D²) . Make each graph a scatter plot and fit a trend curve. The graphs will NOT BOTH be linear. Record the equation of each trend curve and its correlation coefficients (R²) in the spaces below.

When stating your equations, use these variables (NOT y and y):

I for illuminance
D for distance
1/D² for the reciprocal of the distance squared

Refer to the following information for the next two questions.

Graph of Illuminance vs Distance

equation

correlation coefficient (R²)

Refer to the following information for the next two questions.

Graph of Illuminance vs 1/D²

equation

correlation coefficient (R²)

Which graph was linear?

Illuminance vs Distance Illuminance vs 1/D²

Which graph had the better correlation coefficient (R²)?

Illuminance vs Distance Illuminance vs 1/D²both graphs had the same R²

Conclusions

We now return to your data from the paper screen in Part I. Since the same number of lumens illuminated the areas of both the small and large circles we can see how well all of our data conforms to an inverse-square relationship.

Start by substituting the distance of each circle from the light source into either equation generated by EXCEL to calculate the expected illuminance.

small circle's illuminance (lux)

large circle's illuminance (lux)

Calculate the ratio of I_small:I_large. Be careful to state your answer as a decimal with three significant figures.

Next calculate the area of each circle. A = π r²

area of small circle (cm²)

area of large circle (cm²)

Calculate the ratio of A_large:A_small. Be careful to state your answer as a decimal with three significant figures.

Error Analysis

If all of your measurements supported each other then the two ratioes you just calculated in the previous section should be the same. But we do not know THE CORRECT ANSWER; we just know that the two ratios should be identical. Therefore your error should be calculated as the percent difference between your two values.

What was your group's percent difference?

The light probe's manufacturer states that the probe's readings are accurate to ±20%. Using this information, discuss how well your group conducted this experiment.