Effect of varying distance of light source from a Light Dependant Resistor

I'm doing the experiment described here and I have a few questions about it.

I have a miniature light dependent resistor (LDR) hooked to a multimeter set to $\Omega$ and a $25\,\mathrm W$ Light Bulb. By changing the distance between the LDR and the bulb and measuring the resistance of the LDR I made the following plot:

At every $1 \, \text{cm}$, I've taken readings by exposing the LDR to the light for an average time of $10 \, \text{s}$. I waited $20 \, \text{s}$ before taking each subsequent reading. I've conducted the experiment in a dark room and I took every precaution to get accurate readings.

Assuming that the bumpiness was caused by error caused by me while taking the readings, the graph is linear and I think it's safe to assume that

$$R \propto x$$

where $R$ is the resistance of the LDR and $x$ is the distance between the bulb and the LDR.

I understand that this is due to the fact that the intensity of light is decreasing with increase in $x$.

My questions are as follows:

1. How can I correct the bumpiness of the graph? Redoing the experiment yields results of similar bumpiness.
2. Since, $R = kx$, shouldn't this graph when extrapolated pass through the origin? If I average a line through this graph it would be of the form $y = mx + c$ where $c>>0$.
• Do I just say that the nature of how the resistance varies is obvious from my graph or is there some more mathematical way to state it?
• What is the actual equation linking $R$ and $x$?
• Where are the error bars? Why do we see a line instead of data points and a fit? Nov 23, 2014 at 22:43
• @ACuriousMind: The error bars? I'm not sure what you're talking about. The above graph is what I get after playing connect the dots with the scatter plot. There was no point making a scatter plot since all the observed values were concurrent.
– Nick
Nov 23, 2014 at 22:58
• Whenever you do any experiment, you have to include the experimental errors - imprecision of the instruments, error in reading off scales, etc. These will lead to errors on every measurement. "Connecting the dots" is never what we do. You have data points with errors, and you do least-square fits to formulae to determine which relation they obey. (Linear regression if you suspect a linear relation) Doing experiments properly is an art/science in itself. Nov 23, 2014 at 23:12
• @ACuriousMind: I'm looking into all of this right now. Thank you. But even after I take out the error caused by the internal resistance of the LDR and the resistance on the pins of the multimeter, I'm still not getting the graph pass through the origin! What else do I need to consider?
– Nick
Nov 23, 2014 at 23:45
• Have you tried several repeats of the experiment? (Interesting experiment though)
– user60063
Nov 24, 2014 at 10:50

I don't have access to the experiment you linked to, but here are some sources of error I can think of:

1. Distance measurement inaccuracy
2. Variation in angle - depending on the geometry of your "LDR", slight variations in the orientation of your LDR may have a significant effect on the intensity of the received light. Maybe the table you're moving the LDR along has a bump at 14 cm?
3. Reflections - perhaps the light source is complicated by reflections off of walls, ceilings, irregularities in the surface your LDR is on, etc.
4. Heating of the lamp filament - over time, the brightness of an incandescent bulb varies. This could lead to systematic errors if you're always moving in the same direction when you repeat the experiment. Try going the other way and see what happens.

ACuriousMind is right about error bars - if you want to be able to confidently report about your findings, you need to estimate the greatest positive and negative contribution each source of error could give your data points, then add those errors together. Drawing your data as points gives the false illusion that you have determined something precisely. Drawing your data with error bars gives an accurate picture of what you have found.

As for your second question, do you have any reason to believe that the relationship between R and x is linear for all x? I don't know why you would assume that it should remain linear. I also don't understand why you think the intercept should be zero - I don't have the datasheet for your LDR, but I wouldn't assume that either.

• Thanks. I've taken ACuriousMind's suggestion and did a scatter plot and got a perfect line plot out of it through linear regression. The observation table I'm displaying is derived directly from the linearized plot.
– Nick
Jan 3, 2015 at 20:11
• But I still have a problem with the y-intercept. "...shouldn't this plot when extrapolated pass through the origin?" as mentioned in the experiment details. I have an error of $-120\Omega$ which I can't blame on anything. A person I talked to said it was okay since the diode won't become a superconductor at $0cm$ since it's a semiconductor. The book assumes it passes through the origin but no matter how many times I do this experiment, I can't get values like that. What am I missing?
– Nick
Jan 3, 2015 at 20:12
• I would agree with your instructor - it would seem very strange for the resistance to go to 0 Ω, or even very close to that, when you are at 0 cm. Not sure what else to tell you - your data suggests that it doesn't, I wouldn't expect it to, and your instructor wouldn't expect it to. Jan 3, 2015 at 20:18
• @Brionius' answer is quite complete already but I would just add the following comments: 1) there are instrumentation/precision errors, such as the accuracy of your multimeter and ruler, that you can account for by calculating the error and adding appropriate error bars to your plot. 2) systematic errors (such as a bumpy table, reflective walls, stray photons from external light sources, fluctuating light source) that you should eliminate in a repeat experiment. 3) assuming parameter values a priori when doing data fits can be dangerous unless you have a good reason for doing so.
– Dai
Mar 8, 2015 at 7:39
• Also, it looks like you've used excel for your plotting. I don't know how it's fitting algorithm works but I recall that it's not easy to include errors in the fit (especially "x" errors). Have you tried using gnuplot or R?
– Dai
Mar 8, 2015 at 7:41

The light intensity will not vary linearly with distance! As per the inverse square law, R of LDR will increase the dimmer the light though almost certainly not linearly, unless the values of the range used happen to approximate such.

So R should increase with x but not linearly!

• welcome to Physics SE! this answer would be a better answer if you clarified how it does change with distance compared to saying how it doesn't Nov 28, 2019 at 13:22
• While the Light Intensity may vary Inverse sqarely with distance, other than R will increase as the light Intenstiy decreases, I don't know exactly the form of the dependence!! Nov 28, 2019 at 16:37