Aim: to find the refractive index of water

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The refractive index of water

Aim: to find the refractive index of water

Data collection

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)/2=+-0.47

Repeat for other trials I got the following form.

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

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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, ...

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