| Date | May 2011 | Marks available | 8 | Reference code | 11M.2.SL.TZ1.1 |
| Level | Standard level | Paper | Paper 2 | Time zone | Time zone 1 |
| Command term | Calculate, Determine, and State | Question number | 1 | Adapted from | N/A |
Question
Data analysis question.
The photograph below shows a magnified image of a dark central disc surrounded by concentric dark rings. These rings were produced as a result of interference of monochromatic light.
The graph below shows how the ring diameter D varies with the ring number n. The innermost ring corresponds to n = 1. The corresponding diameter is labelled in the photograph. Error bars for the diameter D are shown.
State one piece of evidence that shows that D is not proportional to n.
On the graph opposite, draw the line of best-fit for the data points.
Theory suggests that D2 = kn.
A graph of D2 against n is shown below. Error bars are shown for the first and last data points only.
(i) Using the graph on page 2, calculate the percentage uncertainty in D2, of the ring n = 7.
(ii) Based on the graph opposite, state one piece of evidence that supports the relationship D2 = kn.
(iii) Use the graph opposite to determine the value of the constant k, as well as its uncertainty.
(iv) State the unit for the constant k.
Markscheme
line of best fit is not straight / line of best fit does not go through origin;
smooth curve;
that does not go outside the error bars;
Ignore extrapolations below n=1.
(i) absolute uncertainty in diameter D is ±0.08cm;
giving a relative uncertainty in D2 of \(2 \times \frac{{0.08}}{{1.26}} = 0.13\) or 13%;
Award [2] if uncertainty is calculated for a different ring number.
(ii) it is possible to draw a straight line that passes through the origin (and lies within the error bars);
or
the ratio of \(\frac{{{D^2}}}{n}\) is constant for all data points;
(iii) gradient = k;
calculation of gradient to give 0.23 (accept answers in range 0.21 to 0.25);
evidence for drawing or working with lines of maximum and minimum slope;
answers in the form k = 0.23± 0.03;
Accept an uncertainty in k in range 0.02 to 0.04. First marking point does not
need to be explicit.
(iv) cm2;
