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Aim: to find the refractive index of water

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Introduction

The refractive index of water

Aim: to find the refractive index of water

Data collection

real depth RD/cm

apparent depth AD/cm

RD+-0.05cm

AD+-0.05cm

8.85

6.15

6.30

7.10

6.75

9.30

6.70

7.70

7.65

7.15

9.60

7.95

7.20

6.90

7.05

14.95

11.65

11.90

10.75

12.35

Data processing

For the first trial,

Average apparent depth=(AD1+AD2+ AD3+ AD4)/4

      =(6.15+6.30+7.10+6.75)/4=6.57

Average uncertainty=(ADMAX-ADMIN)/2=(7.10-6.15)

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Middle

Real depth RD/cm

Average apparent depth AD/cm

RD+-0.05cm

AD+-xcm

8.85

6.57+-0.47

9.30

7.30+-0.50

9.60

7.27+-0.52

14.95

11.66+-0.57

image00.png

best-fit gradient: (14.9-8.8)/(11.7-6.6) =1.20

worst fit line with maximum gradient: (14.95-8.85)/( 11.66-0.57-6.57-0.47)=1.51

worst fit line with minimum gradient: (14.95-8.85)/( 11.66+0.57-6.57+0.47)= 1.00

Average uncertainty=(GMAX-GMIN)/2=(1.51-1.00)/2=0.26

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.

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Conclusion

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

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