EuPhO 2023 — Задача 2. E2 - Optical black-box (10 pts)
Автор: Olympiads XYZ · транскрипция на официалните материали
Проверена срещу оригинала на 13.9.2026 от същия модел, който я е транскрибирал (без независима проверка)
7. EuPhO 23 — Experimental Problems - Language: English · 10 т.
Внимание: Бележка към темата
Problem statements are outside this window; assembly must replace '[извън прозореца]' placeholders. Task 4 solution continues beyond page 6 (grading table E1.4 and figure captions printed on page 6; remaining solution pages 7-11 in another window).
Условие
WARNING!
Do not open the black-box. Do not shake the black-box. Do not touch the windows of the optical ports. If you break the black-box or the windows or attempt to open the black box, you will be disqualified.
Your task is to determine the contents of an optical black box without opening it.
The black-box has four optical ports (A, B, C and D) for light, and two optical axes (Fig. 2). The optical axes are perpendicular to each other. There is up to one optical element behind each of the ports as well as another one in the center of the box. You can use a laser and a laser mount with a wheel (that you can put marks on it with a pencil) in order to rotate the laser.
Equipment (see also Fig. 4)
A Black-box
B Laser module in mount with wheel (the same laser module is used for both experiments, to be placed on the table surface)
C Transparent block
D Masking tape, pencil, ruler, paper with diagonal scale
Do not look directly into the laser beam, and make sure no other people are hit by it. Do not look into the optical ports of the box if the laser is on, and turn the laser off when not needed.
Table 1: Possible elements in the slots of the black-box
| no element | there is just air in the slot |
|---|---|
| mirror | angle between the mirror axis and one of the optical axes |
| prism | angle between one of its sides and one of the optical axes of the black box, shaped like regular triangle |
| concave or convex lens | distance to the center of the box, magnitude and sign of the focal length. Note: Axes of lenses are always along optical axes. |
| polarizer | angle of orientation relative to the vertical axis of the black-box |
| single, thin slit | distance to the center of the box, width of the slit |
| diffraction grating | distance to the center of the box, direction of stripes, distance between the stripes |
| pin hole | distance to the center of the box, hole diameter |
Important hints:
- The wavelength of the laser is .
- The refractive index of transparent elements can be assumed to be 1.5.
Note: The laser module is initially mounted to the setup for E1. You have to take it off so you can use it for E2. You can also put it back (pay attention to alignment) when you want to switch back to E1.
Task E2.1 - Central element (~0.3 pts) The two optical axes cross in the center of the black box. At the crossing could sit: no element, a fully reflective mirror (both sides), a semi-transparent mirror, or a regular-triangle-shaped prism.
Determine which element is placed centrally in the black box. Describe its orientation towards the optical ports (A, B, C, D) - for example by using a sketch. Justify your choices. [0,3 т.]
Task E2.2 - Elements in remaining slots (~2.2 pts) There is one element from Table 1 in each of the four slots behind the optical ports A, B, C, D, respectively.
Determine for each slot the type of element present. Justify your choices. [2,2 т.]
Task E2.3 - Properties (~7.5 pts) In Table 1, you can find a second column containing characteristic properties of the possible elements.
Determine these characteristic properties for the optical elements used inside the box at slots A, B, C and D as precisely as possible. [7,5 т.]
Решение
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Оригинал в Архива: eupho2023_experiment_problems.pdf · официални решения: eupho2023_experiment_solutions.pdf