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Using the CBL and the TI-83

To Find The

Mathematical Relationship

Between The

Intensity

of a Light Source And the

Distance

From the Source 20 July 2L+3

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A. Gathering Data

1. Connect CBL to TI-83

2. Connect probe to CBL

3. Load and use program to control CBL

4. Learn how to collect data

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B. Set Desired Graphing Mode

“MODE”

“Normal” “Float”

“Degree” “Func”

“Connected” “Sequential”

“Real” “Full”

“2nd”, “QUIT”

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C. Clear Data from Lists

1. “Stat”, “1:Edit”

2. Move cursor over heading, L1

3. “Clear”, “Down arrow”

4. Move cursor to heading of other columns and repeat steps 1, 2 and 3.

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D. Enter Data

1. Enter distance data in L1

2. Enter intensity data in L2

Record this information.

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E. Clear Previous Graphing Commands

1. “Y=”

2. Move cursor to each Y_ that has an equation in it, then “Clear”

3. “2nd”, “Stat Plot”

4. “4:PlotsOff”, “Enter”

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F. Graphing Data

1. “2nd”, “Stat Plot”

2. Select “1:Plot1...Off”

3. Select “ON”

4. For type, select first graph (points only)

Selecting second graph will plot points and connect them with a straight line.

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F. Graphing Data -2-

5. for Xlist: select L1 (distance)

6. for Ylist: select L2 (intensity)

7. for Mark: select square

8. “Graph”

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F. Graphing Data -3-

If data points not seen or if data points do not occupy most of screen:

9. “Zoom”, “9:ZoomStat”

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G. Analysis of Data

What is the shape of the data points?

Do the points form a straight line? Through the origin (0,0)?

What is the shape of the points?

a hyperbola.

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G. Analysis of Data -2-

This means that there is an inverse relationship between the intensity of light and the distance from the light source.

So lets plot the intensity of light vs the inverse of the distance from the light source.

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H. Creating Adjusted Data

1. “Stat”, “1.Edit:”

2. Move Cursor over L3

3. “2nd”, “L1”, “x-1”

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I. Graph New Data

1. “2nd”, “Stat Plot”

2. Select “1:Plot1...On”

3. Select “Off”, “Enter”

4. “2nd”, “Stat Plot”

5. Select “2:Plot2...Off”

6. Select On

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I. Graph New Data -2-

7. For type, select first graph

8. for Xlist: select L3 (1/distance)

9. for Ylist: select L1 (intensity)

10. for Mark: select square

11. “Zoom”,

12. “9:ZoomStat”

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J. Analysis of DataWhat is the shape of the data points?

This means that there is an inverse power relationship between the intensity of light and the distance from the light source.

It is a parabola.

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K. Creating Additional Adjusted Data

So lets plot the intensity of light vs the square of the inverse of the distance.

1. “Stat”, “1.Edit:”2. Move Cursor over L4

3. “2nd”, “L3”, “x2 ”

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L. Graph New Data

1. “2nd”, “Stat Plot”

2. Select “2:Plot2...On”

3. Select “Off”, “Enter”

4. “2nd”, “Stat Plot”

5. Select “3:Plot3...Off”

6. Select On

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L. Graph New Data -2-

7. For type, select first graph

8. for Xlist: select L4 (1/distance2)

9. for Ylist: select L1 (intensity)

10. for Mark: select square

11. “Zoom”

12. “9:ZoomStat”

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M. Analysis of Data

The data points look like they form a straight line.

This implies that the intensity of light is inversely proportional to the square of the distance plus some constant.

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M. Analysis of Data -2-

Since the equation of a straight line is:

y mx b

Id

b 12

We can then say:Lets now find the value of b?

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M. Analysis of Data -3-

To see all of the 1st quadrant: 1. “Window” 2. Set x-min to zero. 3. Set y-min to zero. 4. Graph Does it appear that the line goes

through origin?

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M. Analysis of Data -4-

If so, then:

and from it:

Where k is the slope of the line.

Id

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I kd

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N. Finding the Slope of the line.

1. “STAT”, “>“, to 'CALC'

2. “5.LinReg(ax+b)

3. “2nd” “L4” “,” “2nd” “L2”

4. “Enter”

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O. Examining Information

1. The slope is ‘a’. 2. The y-intercept is ‘b’. 3. Write them down.

4. The final equation is:

where ‘a’ is the value of k.

I kd

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O. Examining Information -2-

‘r’ is called the correlation coefficient

If the value of ‘r’ is 1.000, then all the data points fall exactly on the calculated line of best fit.

The further the value of ‘r’ is from 1.000, the less reliable are the data points.

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P. Drawing the Line of Best Fit

1. “Y=“, “VAR”

2. “5:Statistics...”

3. “>“, “>“, (to EQ)

4. “7:RegEQ”, “Graph”

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Q. A Shortcut

1. Complete steps through F.

2. “Stat”, “Calc”, “B:PwrReg”,

3. “2nd”, “L1”, “2nd”, “L2,”, “Enter”

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Q. A Shortcut -2-

5. Substitute:

‘I’ for y ‘d’ for x

value of a for ‘a’

value of b for ‘b’

6. How does this equation compare to that found earlier?

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Q. Recalling Saved Data.

1. “2nd”, “DRAW”, “>“, “>“, to 'STO'.2. “4:RecallGDB”, “Enter”3. “VARS”, “.GDB...”, “Enter”4. Choose appropriate 'GDB_' in which

data was stored that you wish to recall.

5. “Enter”