The next method used to obtain the focal length of the same convex lens was the following: the meter stick was placed on a table in a darkened room. The lens holder (with lens) was placed at a point on the ruler. A lit candle was placed on one side of the lens (on a candleholder) and on the other, the cardholder (with card). The cardholder was then moved along the meter stick until the image on the card was focused enough to show details (i.e. the flame, the reflection on the molten wax, etc.). This entire process was repeated three times with the candle at different distances from the lens. Again, the Lens Equation was used to find f for each trial. Then this entire method was repeated with the same second double convex lens as in the last procedure.
Data:
(Note: In the “w/ sunlight” trials, the Lens Equation was not applied to find f, for the distance from the real image to the lens was already f. So to find f, all that was done was find the distance between the mark at which the lens was at from the mark where the card was at by using simple subtraction.)
Double convex lens I
W/ sunlight:
Lens: 14.00 ± 0.1 cm mark
Focused real image on card: 24.10 ± 0.5 cm
So, f: 10.10 ± 0.6 cm
Double convex lens II
W/ sunlight:
Lens: 45.00 ± 0.1 cm mark
Focused real image on card: 35.49 ± 0.1 cm
So, f: 9.51 ± 0.6 cm
Double convex lens I & II
W/ candle trials: Trials 1-3 in the below table refer to the trials completed with lens I and Trials 4-6 in the same table refer to the trials completed with lens II.
*Calculations in below table:
Found using the Lens Equation: 1/do + 1/di = f.
I.e. Trial 1: [(1/22.48) + (1/18.00) = (1/f)], so
(0.445 + 0.555) = 0.100 = (1/f), so
f = (1/0.100), so f = 9.99.
-----------------Raw Data-------------------- --------Calculations--------- Results
# Please note: In trials 1-6 the lens was always placed at the 45.00 ± 0.1 cm mark, this extra ± 0.1 cm uncertainty was considered when calculating uncertainty for each trial.
Uncertainty: For all of the trials in this laboratory investigation, it is clear that there is too much human judgment involved in focusing the image. The investigators, when moving the lens (in double convex lens I), the cardholder (double convex lens II), and candle (double concave lens) several mm could not be absolutely sure that the focus was worse or better. This tactual experience definitely added to the uncertainty of the results obtained during experimentation. As a result, the di’s found in all trials had a greater uncertainty than that of the lens positions (all trials), card positions (“w/ candle”), and do (all trials), whose uncertainties were estimated to be at ± 0.1 cm because a meter stick with a precision of millimeter was used. It is important to note that the card position uncertainty in the “w/ candle” experiments was ± 0.5 cm due to the “tactual experience” referred to earlier.
I.e. In “w/ candle”, Trial 1:
# Note: The lens was placed at the 45.00 ± 0.1 cm mark.
The final calculated uncertainty in Trial 1 was calculated like this:
-
do has an uncertainty of ± 0.2 cm because it is calculated by subtracting 45.00 ± 0.1 cm (lens position) from 67.48 ± 0.1 cm (candle position), so when those two uncertainties are added, they give a total uncertainty of ± 0.2 cm
-
di has an uncertainty of ± 0.6 cm because it is calculated by subtracting 27.00 ± 0.5 cm (card position) from 45.00 ± 0.01 (lens position), so when those two uncertainties are added is added, they give a total of ± 0.6 cm uncertainty.
- 0.2 cm is approximately 1% of 22.48 cm
- 0.6 cm is approximately 3% of 19.00 cm
-
1% + 3% = 4%, so the total uncertainty for this Trial 1 is ± 0.6 cm because 4% of 9.99 is 0.6.
This same process to find final uncertainty was repeated for every trial.
Results/Conclusion: All the results (f’s) found using Lens I, in both the sunlight and candle trials, were in the estimated range of uncertainty, as was the case for all trials using Lens II. As a result the hypothesis of this laboratory experiment was shown to be correct: the Lens Equation, 1/di + 1/do = 1/f, did, in fact, produce equal f’s for the same lens.
Evaluation: The lab equipment used in this experiment was not exactly grade-A material—the metal clips attached to the lens holder, cardholder, and candleholder were all rather rickety, causing the objects they were holding to not be as straight as they could be. Also, in the “w/ sunlight” trials, the investigators, in an ideal scenario, should have been using light from infinity, but instead were focusing on the walls of buildings and the leaves on trees about 50-100 meters away. The use of candles as a light source is also something that could be improved on because candlelight flickers and therefore adds to the difficulty of focusing the image correctly. Furthermore, because there were only a few trials performed on a meter-stick, which restrained the distance to only 1-meter, the margin of error was greater than it could have been.
Suggestions: This laboratory experiment could have been improved by using optics benches instead of the flimsy metal clips and the meter stick used in this lab. Also, though it is impossible to focus on light from infinity, the investigators could have focused on something further away, such as a passing airplane. Perhaps a transparent light bulb could have been used instead and in this manner, the laboratory investigators could look at the light-producing wire, which does not shine as intermittently as candlelight does.
In addition to all of the above, some more trials could have been performed, and it would have been better to work with larger distances instead of being restrained by a meter stick, because although the same uncertainties would have been applied to the lens positions (all trials), card positions (Part A, “w/ candle”), and do (all trials), ± 0.1 cm uncertainty in a distance of, say, 5-meters would constitute a smaller margin of error than in merely a 1-meter distance.
