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

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)/2=+-0.47

Repeat for other trials I got the following form.

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

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.