(i) Outline why OY has a greater percentage uncertainty than OX for each pair of data points.

(ii) The refractive index of the water is given by \(\frac{{{\rm{OX}}}}{{{\rm{OY}}}}\)when OX is small.

Calculate the fractional uncertainty in the value of the refractive index of water for OX = 1.8 cm.

A graph of the variation of OY with OX is plotted.

(i) Draw, on the graph, the error bars for OY when OX = 1.8 cm and when OY = 5.8 cm.

(ii) Determine, using the graph, the refractive index of the water in the container for values of OX less than 6.0 cm.

(iii) The refractive index for a material is also given by \(\frac{{\sin i}}{{\sin r}}\) where i is the angle of incidence and r is the angle of refraction.

Outline why the graph deviates from a straight line for large values of OX.

i
OY always smaller than OX AND uncertainties are the same/0.1
« so fraction \(\frac{{0.1}}{{{\rm{OY}}}} > \frac{{0.1}}{{{\rm{OX}}}}\) »

ii
\(\frac{{0.1}}{{{\rm{1.3}}}}\) AND \(\frac{{0.1}}{{{\rm{1.8}}}}\)
= 0.13 OR 13%

Watch for correct answer even if calculation continues to the absolute uncertainty.

i

total length of bar = 0.2 cm

Accept correct error bar in one of the points: OX= 1.8 cm OR OY= 5.8 cm (which is not a measured point but is a point on the interpolated line) OR OX= 5.8 cm.
Ignore error bar of OX.
Allow range from 0.2 to 0.3 cm, by eye.

ii

suitable line drawn extending at least up to 6 cm
OR
gradient calculated using two out of the first three data points

inverse of slope used

value between 1.30 and 1.60

If using one value of OX and OY from the graph for any of the first three data points award [2 max].
Award [3] for correct value for each of the three data points and average.
If gradient used, award [1 max].

iii

«the equation n=\(\frac{{{\rm{OX}}}}{{{\rm{OY}}}}\)» involves a tan approximation/is true only for small θ «when sinθ = tanθ»
OR
«the equation n=\(\frac{{{\rm{OX}}}}{{{\rm{OY}}}}\)» uses OI instead of the hypotenuse of the ∆IOX or IOY

OWTTE