Investigation about the inverse square law of light radiation

[supersub]

Homework Statement

*Main ideas in bold[/B]
Investigation of the inverse square law of light radiated from a light bulb. (done method, diagram, results and graph)

Independent variable = the distance from the LDR (cm)
Dependent Variable = resistance (k/ohms)

Brief method: using an LDR, bulb, power supply and a resistance metre, get a range of results of the resistance by moving the bulb closer and closer to the LDR e.g. I did first reading 2cm from LDR and then went up by 2cm each time to 20cm. Then plot results on a graph and use it to verify the theory p=k/[d][2].

The Graph is nearly a straight line positive correlation where it sort of curves in the positive direction from 2-6cm/20cm, then is pretty much linear, not sure if this is how its meant to be.

The main issue I have is how to find (k), the constant and how to use my results and graph to verify the theory.

ps. that method isn't my original I just tried to summarise as it would have been long

Homework Equations

Theory being p=k/[d][2] where: p= intensity d=distance between the LDR and the bulb and k= constant
Inverse square law - I ∝ 1/[d][2]

The Attempt at a Solution

To be honest I haven't done this kind of practical in a long time due to it being the first one of the year so I don't know where to start but i think I need some help with the first step or 2 and I'll remember.

 

[haruspex]

You mention a resistance as the dependent variable, but the equation you quote has power. What exactly did you plot? Was the Y axis resistance, or inverse of resistance (or...?). Was the X axis distance or inverse of distance, or inverse of squared distance, or...?
If you could post an image of the graph it will help.

 

[supersub]

You mention a resistance as the dependent variable, but the equation you quote has power. What exactly did you plot? Was the Y axis resistance, or inverse of resistance (or...?). Was the X axis distance or inverse of distance, or inverse of squared distance, or...?
If you could post an image of the graph it will help.

These are pictures of the write up sheet, that's my table of results there and i used the resistance for the y-axis and distance for the x-axis as it is on my results but now I am not so the sure, I couldn't get a picture of the graph as it won't come out right but it is pretty much a linear positive correlation the slight curve is, or could be due to errors i was thinking. Also the equation is shown in part f, I think the main things I am going to have trouble with is part f and part k.

Thanks for helping!
ps. sorry about the quality i=as I took it from my phone.

 

[haruspex]

I couldn't get a picture of the graph as it won't come out right

Then take the trouble to type the table of numbers into a post so that readers can copy them into a spreadsheet.

 

[supersub]

Then take the trouble to type the table of numbers into a post so that readers can copy them into a spreadsheet.

I did its in one of the pictures the table of results and now I've added the graph now seems ok. X-axis being the distance between ldr and bulb and y-axis being the resistance in Kohms.
I haven't done the line of best fit yet just until I am sure how it should be

 

[haruspex]

I did its in one of the pictures

I asked you to type the numbers into a post. I cannot cut and paste numbers from an image.
How will you find the line of best fit? If you believe it should be a quadratic, you can plot the y value against x² and expect a straight line fit.

 

[supersub]

Ok
Distance from LDR to filament bulb (x) in cm: Resistance in kohms (y)

1. 2-------------------------------43.3
2. 4-------------------------------45.6
3. 6-------------------------------53.0
4. 8-------------------------------60.2
5. 10------------------------------69.1
6. 12------------------------------82.3
7. 14------------------------------96.1
8. 16-----------------------------107.0
9. 18-----------------------------116.1
10. 20-----------------------------125.7

I'm thinking I need to to the inverse 1/[x[2] for all x values and then plot the graph then find the gradient which should be the value k in the equation, and then see if my results add up to the constant, k.

 

[supersub]

Ok
Distance from LDR to filament bulb (x) in cm: Resistance in kohms (y)

1. 2-------------------------------43.3
2. 4-------------------------------45.6
3. 6-------------------------------53.0
4. 8-------------------------------60.2
5. 10------------------------------69.1
6. 12------------------------------82.3
7. 14------------------------------96.1
8. 16-----------------------------107.0
9. 18-----------------------------116.1
10. 20-----------------------------125.7

I'm thinking I need to to the inverse 1/[x[2] for all x values and then plot the graph then find the gradient which should be the value k in the equation, and then see if my results add up to the constant, k.

 

[J Hann]

The straight line portion looks good.
Perhaps the results, for the smallest values of x, should be ignored.
The inverse square law relates to "point" sources, so maybe for the smallest values
of x the results are being skewed by an "extended" source.