Investigation: Light Intensity Decay Over Distance

Why Is Alaska So Cool? Distance Intensity Investigator

Activity 6: Distance Intensity Investigator

Investigations in Light Intensity Change Over Distance

Guiding Question

How does the intensity of light change as the distance from the light source increases?

Prediction of Results

Predict what you think will happen and what type of equation and graph might best fit the data representing the intensity of a light as the distance from the light source increases.

Objective

After completing this lesson, a student should be able to analyze light intensity striking a surface at varying distances from the light source.

Materials

CBL, TI-83 Plus calculator, light sensor, lamp with light bulb (60 to 100 watts), tape measure, masking tape (or other type), wood block or other item to attach light sensor to, BULB program, daily log

Vocabulary

intensity decay power regression

Introduction

There are two parts to the introduction in this lesson. Part 1 instructs in the set up and use of the CBL, and Part Two concerns the investigation of light intensity itself.

Part 1 -- The CBL

CBL stands for “calculator based laboratory.” It has powerful onboard computer chip that operates the unit. The CBL unit is an expensive and precise instrument so please use it with care and do not mishandle it. You need not be afraid to use it properly as it is sturdy for the purposes intended, but keep it always in its protective box when you are not using it.


Please open the CBL protective case, a black, tough plastic box. You will see several items in the case:

·  the CBL unit itself

·  three sensors

o  a light sensor

o  an electrical probe

o  a temperature probe

·  a black link cable (also called a unit-to-unit cable)

You will be using only the light sensor for all activities in the projects ahead. The light sensor has a flat electrical wire attached to it that has LIGHT written near the connector end. You will not need the other probes, so you may leave them in the case.

If you have not already done so, please remove the CBL unit, the light sensor, and the black link cable from the protective case. The link cable has a mini-phone plug at either end. Set the case aside.

Now take a good look at the CBL, as the CBL figure below represents.

Notice that it has a digital display read-out and five keys just below its screen. Around the screen on three sides are ports (places to plug in devices) named, CH1, CH2, CH3, SONIC, DIG IN, and DIG OUT. The only port you will be using is CH1, at the top of the unit.

At the bottom of the unit are two more small ports. The one to the right is for power (you will not use it); you will use the one to the left as it connects the CBL to your TI-83 Plus calculator with the enclosed cable.

Please turn on the CBL. Do this by pressing the red ON/OFF button at right. The display immediately shows some dashes, numbers, or words. These may change depending upon the last measurements that were done with the CBL.

Now turn the CBL off. Please do this by pressing the blue 2nd button at left (it acts as a shift key), followed by pressing the red ON/OFF button. The screen turns blank. When you press the blue button, you can know that the button has engaged because“ 2nd ” displays in the upper right corner of the screen. If you did not press the blue button completely, the display simply flickers momentarily when you then press ON/OFF, but does not turn off. Make sure the CBL is turned off so that there is a blank screen.

Please take the light sensor now, and plug it into the CH1 port of the CBL. It works similarly to a telephone jack. Note that it will insert only one way. Never force the connector plug into the port. If it does not plug in easily, then you either are trying to plug into the wrong port or you have the connector upside down. The various ports are designed to accept a particular type of connector so that various probes are identified correctly by the CBL’s processor. (All three CH ports will accept the light sensor, but in these investigations you must use only CH1, please.)

To remove the sensor, press the small lever on the connector that locks the sensor into the port, and pull the connector out. It should slide out easily. If it does not slide out easily, do not force it. It just means you have not released it properly yet.

Now take the black link cable and insert one end with the mini-phone jack into the left port at the bottom of the CBL. Press it in firmly so that you may feel a little “click” when it is firmly seated.

If you do not already have it, get your TI-83 Plus calculator. Take the other end of the link cable, and press it in into the port on the calculator. You should feel the “click.” The link cable port is on the bottom edge of the calculator. The linked instruments should look like the figure at right.

What you have just done, plugging in the connector and cable, and turning the CBL on or off, are the only actions you will need to take on the CBL itself. Everything else will be controlled by the TI-83 Plus calculator. As you will see, the TI-83 Plus has the capacity to program the CBL through the cable so that the CBL will accomplish the tasks we want it to do.

Introduction Part 2 – Intensity Investigation

Light intensity is the “brightness” of a light. It is the amount of light shining on a surface. More precisely, intensity is the rate at which energy is transferred per unit area, typically measured in watts per square meter, W/m2. (In this investigation, we will measure it in milliwatts per square centimeter, mW/cm2.)

As light propagates (moves) away from its source, the associated light energy tends to spread out. Consequently, the intensity of the light (I) decreases as the distance (d) from the source increases. Intensity decay is the lessening of brightness. This investigation uses a light intensity sensor to identify the relationship between the intensity of light and the distance from its source.

Equipment Setup Procedure

Please gather the materials indicated at the beginning of this lesson. You will also use a program called BULB that may already be present in the calculator. If it is not, you may download it from this web site.

Set the equipment as shown in Figure 1.

1.  Connect the CBL to the calculator with the unit-to-unit (black link) cable using the input/output ports located on the bottom edge of each unit. Press the cable ends in firmly.

2.  Connect the light probe to CH1 on the top edge of the CBL.

3.  Secure the light sensor to a wooden block with tape. Position the sensor so that it is facing the light bulb at the same height as shown in Figure 1.

4.  Stretch out the tape measure on a table, floor, or other suitable level surface so that the measuring tape forms a (straight) line from the bulb to 2 m away from the bulb. If your tape measure is not 2 m long, you may measure the first meter out, then tape the nearer end of the tape measure at the 1m mark, and tape the far end of the tape measure in a direct line away from the bulb.

5.  With masking tape or other tape, mark 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, and 2.0 m intervals along the tape measure.

6.  Position the light sensor so that the separation between it and the center of the bulb is 1 m. Turn on the light bulb.

7.  Turn on the CBL and the calculator.

The CBL is now ready to receive instructions from the calculator’s program. Some of the next directions will help you make sure you have made secure connections.

Experiment Procedure

  1. Make sure the CBL and the calculator are turned on.
  2. On the calculator, press to see the programs available to you. You will see a screen similar to the one below (you may have other programs also):
  1. Choose the 2:BULB program by pressing or by moving the cursor to 2:BULB with the up/down ( ) cursor keys, and pressing the calculator key when the cursor is on BULB. You will see the screen below:
  1. Press , and the following screen shows up:
  1. Press again to see the following screen:
  1. Choose 1: Collect Data by pressing .
  1. Press to choose 1:Yes, and follow the instructions on the calculator screen.
  1. As you complete each screen of instructions, press . The next couple of screens are below.
  1. If you come to a screen similar to the following, recheck the connectors as it explains, then press .
  1. When a screen says STATUS: OK, like either screen below, you continue by pressing
    .
  1. The next screen is as follows. Do what it says, if you have not done so already, and press . Note: Where it speaks of a meter stick, you have used a tape measure instead. You do not need to use a meter stick. “Worksheet” is this lesson plan.
  1. Follow the next screen’s instructions, and press .
  1. And now, you are almost ready. Press , the next screen shows as follows:
  1. You are now ready to begin data collection. Ensure once again that your sensor is at the proper distance from the light. You will take a total of eleven (11) samplings or readings at increasing interval distances of 0.1 m. When you are ready, press
    .
  2. At this point you did not notice it, but when you pressed the button, the CBL instantly sampled the light intensity and stored its value in the calculator. The next screen pops up:

Notice that the calculator screen shows TRIAL 2, and you are instructed to move the sensor to the 1.1 m point. Follow the instructions. As you continue to press on the calculator, the calculator will prompt you at each subsequent trial to move the light sensor and to ready you for each of the subsequent samplings. Continue to follow the instructions on the calculator screen now.

  1. After Trial 11, you are presented with a screen similar, but not identical, to the following:

You have completed collecting your data, and are now ready to analyze the data. You may turn off the CBL, disconnect it from the calculator. Your data are stored in the calculator so that you may turn the calculator off with the data safely inside. If you do this investigation again, you will find that new data replaces the older data. Please return the CBL, light sensor, and link cable to the protective case before proceeding.

Data Record

Data Table: Observations

You noticed that after the data were collected, a plot of light intensity (mW/cm2) versus distance (m) appeared on the calculator screen. The plot looked similar to the one shown in Figure 2.

The calculator has stored the distance and light intensity values in its data tables. To view these values, turn on the calculator. Press the button, and the next screen shows up:

Choose EDIT and 1:Edit. To do this, simply press . The screen that shows up is similar but not identical to the following.

The column L1 shows the distance in meters (m) from the light bulb. Column L2 shows the light intensity values in milliwatts per square centimeters (mW/cm2). (Other columns, such as the L3 column above, are not used in our experiment so you may or may not show values. It does not matter.) Though your L1 will be the same as the screen shot above, it will surely not be the same as L2. The paired values are in rows, so that in the experiment above, the light intensity at 1 m was .86247 mW/cm2, at 1.1 m was .84503 mW/cm2, and so on.

You may scroll through the values using the up/down cursor keys.

Mathematical Analysis

You will conduct now a regression analysis. Recall that a regression analysis is an attempt to develop a mathematical equation that best describes the data points collected. Note: To review how to do regression analysis with the calculator, refer to Activity 1: TI-83 + DATA = MODEL, Introduction to Computational Science and Mathematical Modeling Using the TI-83 Plus Graphing Calculator.

You have likely noted that if you connected your data points in Figure 2 above, the result would resemble a curve approaching the x-axis. The question is: In looking at this curve, what type of graphed mathematical equation might we say Figure 2 resembles? As you consider the curve you may note that intensity values approach, but never quite reaches, 0 mW/cm2. You also note that you could keep getting closer to the light source (and in the real world you could actually get to the light, but you would never get closer to the light than the light itself!).

From your studies in algebra you might think of several mathematical possibilities. To review possible types of graphs, try entering the following functions one at a time in and pressing to see what type of equation might best represent the data:
y = x, y = x2, y = x3, y = x4, y = , y = , etc. Press , then to zoom in around the origin. Are any of these graphs types that might model the data in a predictable fashion? Recall that a linear regression equation is of the form y = ax + b. On the TI-83, the QuadReg is of the form y = ax2 + bx + c, the CubicReg is of the form y = ax3 + bx2 + cx + d, and the QuartReg is of the form y = ax4 + bx3 + cx2 + dx + e. All of these are types of polynomial regressions.

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