So the refractive index is 1.20+-0.26
Percentage uncertainty=0.26/1.20=21.7%
Percentage discrepancy=(1.33-1.20)/1.33=9.8%
Conclusion
So there is a proportional relationship between apparent depth and the real depth. The gradient shows the experimental value of the refractive index of water is 1.20+-0.26.
The systematic error could be the thickness of the mirror. Then, the position of the virtual image in the water will appear to be higher then the actual one. This will affect the apparent depth and thus the refractive. The other systematic error is the bulge of the middle part of water compared to area all around. Like the first one, this could also influence in the measurement of the apparent depth. Random error can be the depth of the water. Sometimes, even though I felt like I already filled the cup to the top, it’s very hard to control that. Thus the real depths may not be the heights of the cups. Second random error is the human error because I used my eyesight to judge whether two images are in the same size.
The percentage discrepancy of 9.8% is much smaller than the percentage uncertainty of 21.7%. The experimental value 1.20+-0.26 compensates the actual value 1.331. So this means that the result I got is pretty accurate. From the graph it is clear that the line will continue climb up straightly forming a straight line.
Evaluation
1 process: since I relied on my eye sight in the whole process to adjust the position of the upper pin, it could lead to inaccuracy because I couldn’t make sure I observed from the same point.
2 equipment: I used a cork to fix the upper pin. However, this means that a part of the pin will need to go into the cork. Thus, the length will be shorter than the other pin.
3 time management: it is not significant in this experiment. However, because I also had 4 cups I only did 4 trials. It would be better if I can find more cups to do more trials in order to get a more reliable result.
The experimental value 1.20+-0.26 compensates the actual value 1.331. So the weaknesses talked above aren’t very significant. This means that the result I got is high-quality data. For accuracy, since the final value is very close to the actual one, it can be said that the data is pretty accurate. In term of precision, since the best-fit line is in the “error bars”. (all the points don’t fluctuate about the best-fit line)
Improvement:
1 for experimental techniques, I should set up a stand or similar thing so that I can observe from the same spot all the time. Because of the fact that I still have to watch on two pins to compare their sizes, the problem of random error will still exists.
2 I should change the cork into a magnet next time so that it can attract the pin without changing the length of it. Then two pins will just be in the same size removing a systematic error.
3 from the graph it’s shown that my three previous values are quite close to each other and the forth one appears to be far away. Next time, I should find more cups with bigger difference in sizes compared to each other. Then, the data range will also increase, improving the accuracy. More trials can also reduce some random errors.
4 in choosing the mirror, I should choose the one as thin as possible. So thin that the thickness of it can be ignorable and this can help me get a bigger control both independent and dependent variable.
Reference
1 http://hypertextbook.com/facts/2005/AmyHo.shtml