For λ = 5.0 X 10^5m calculate the (i) fractional uncertainty in d. (ii) percentage uncertainty in d^2 ?

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1 Answer
May 10, 2018

See below:

Explanation:

For (i):

From my measurement by eye, it seems that the point where lambda=5.0 times 10^5, y=0.35 cm. The bars stretch up until 0.4 cm so the fractional uncertainty on the measurement should be approximately +- 0.05 cm

So the fractional uncertainity is:

0.05/(0.35) approx 0.14 (as a fractional uncertainty, 14% as a percentage uncertainty)

Uncertainties:

When two values are multiplied with uncertainties use the formula (Section 1.2 in the Physics Data booklet):

as d^2= d times d

If

y=(ab)/(c)

Then the uncertainties are:

(Deltay)/(y)=(Deltaa)/a +(Deltab)/(b)+(Deltac)/c

hence:

(Deltay)/(0.35)^2=(0.05/0.35)+(0.05/0.35)

(Deltay)/(0.35)^2=0.1/0.35

(Deltay)/(0.35)^2 approx 0.28 so the percentage uncertainty is 28% or the fractional uncertainty is 0.28.