Light Intensity vs. Distance

**You will need: **The **EA-100** with the light probe attachment, the **CASIO CFX-9850G** calculator, a working flashlight, a tape measure, a wooden
block, and masking tape.

**Procedure: **Turn the flashlight on and place it on the floor. Darken the room. Using
the light probe and the tape measure, sample the light intensity at different distances
from the light source. Keep a record of these data. It is useful to keep the light sensor
at the same height, pointing towards the center of the light source; to do this tape the
light sensor to a wooden block or similar object. It is also useful to take the average
reading, say the average of 10 readings, at the different distances, to minimize
variation. Use the program EZEPERI to sample the light intensity by entering 2 for new
experiment, 1 for the channel, 1 or 9 for the operation, 3 (STATS) for post-processing, 10
for statistic sample size, 1 second for time, and 1 for the sample size. Keep track of the
entries in List 2, which will be the average light intensity of the 10 readings. Also for
each of the light readings keep track of the distance to the light source.

Enter the distance data into List 1, and the light intensity into List 2.
"Normalize" the light intensity data (i.e., divide by the largest intensity
value); this will allows the use of a smaller viewing window for easier comparisons
between samples. To enter the normalized data into List 3, highlight the List3 title using
the cursor arrows. Assuming the largest value of intensity is on cell 1 of List 2, press **OPTN
F1** (LIST) **F1** (List) **2 ÷ F1** (List) **2 [1] EXE**. The normalized data
is saved into List 3.

To draw the scatterplot press **MENU**, use the cursor arrows to highlight the STAT
icon, and press **EXE**.

Press **F1** (GRPH) **F6** (SET) and set the parameters as follows:

StatGraph1

Graph Type :Scatter

XList :List1

Ylist :List3 (This is the normalized data)

Frequency :1

Mark Type : (This is your choice)

Graph Color : (This is your choice)

Press **EXIT** **F1** (GPH1).

Many questions can be asked of the data. For example:

- Is the intensity increasing or decreasing as the light source is farther away? What is the sign of the derivative of this function?
- Approximate numerically the derivative of the light intensity function with respect to distance. Use the numerical derivative to approximate the light intensity at different distance.
- Can you match a function to the data?