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第26届国际物理奥林匹克竞赛理论试题及解答（英文）
Theoretical Question 1
This is essentially a question in special relativity. The core of the question is part (b) which involves a simulated experiment. It requires students to combine the concepts of gravitational red shifts, resonance absorption, Doppler shifts and the graphical interpretation of data.
Overall the question appears to have met its objective of allowing nearly all students to gain a few marks from part (a). A suprisingly large number of students were able to obtain essentially the correct solution to part (b) using the appropriate straight-line graph. Part (c) also produced many basically correct solutions with some of the best students simplifying their soloution to the logical limit. One student managed to obtain the correct answer making use of the 4-momentum. The very best answers to this question were almost °awless and demonstrated a very high level of conceptual understanding and the ability to synthesise ideas from a number of di®erent areas.
Theoretical Question 2
This question is concerned with the propagation of waves in a medium with a varying refractive index and the di®erent modes of propagation which occur. The responses to this question mirrored the marks distribution shown in Figure 1 for the overall theory results. A number of students gained near-perfect marks while an equivalent number gained very few. The most interesting part of the marking arose in connection with part (a), where the arc radius R speci¯ed in the question needs to be established. The marking team encountered four distinguishable and valid approaches to establishing the result for R.
Part (c) proved to be a useful discriminator between those students who either did, or did not, realise that a seris of paths, or modes, exists from the source to the receiver. The numerical estimates in part (d), and intended to assist the markers, required some care in marking according to the way in which students treated the issue of signi¯cant ¯gures during the calculation. Part (e), which led to the conclusion that the ray with the smallest calue of initial angle will arrive ¯rst, was a useful discriminator.
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