IZhO 2013 — Задача 1. Advertising tricks [15 points]

*IX International Zhautykov Olimpiad/Experimental Competition

EXPERIMENTAL COMPETITION 16 January, 2013

Please read the instructions first: · 16 януари 2013 г. · 15 т.*

Условие

1. The Experimental competition consists of one problem. This part of the competition lasts 3 hours.
2. Please only use the pen that is provided to you.
3. You can use your own non-programmable calculator for numerical calculations. If you don’t have one, please ask for it from Olympiad organizers.
4. You are provided with Writing sheet and additional papers. You can use the additional paper for drafts of your solutions but these papers will not be checked. Your final solutions which will be evaluated should be on the Writing sheets. Please use as little text as possible. You should mostly use equations, numbers, figures and plots.
5. Use only the front side of Writing sheets. Write only inside the bordered area.
6. Fill the boxes at the top of each sheet of paper with your country (Country), your student code (Student Code), the question number (Question Number), the progressive number of each sheet (Page Number), and the total number of Writing sheets (Total Number of Pages). If you use some blank Writing sheets for notes that you do not wish to be evaluated, put a large X across the entire sheet and do not include it in your numbering.
7. At the end of the exam, arrange all sheets for each problem in the following order:

• Used Writing sheets in order;
• The sheets you do not wish to be evaluated
• Unused sheets and the printed question.

Place the papers inside the envelope and leave everything on your desk. You are not allowed to take any paper or equipment out of the room

Equipment: Laser, tripod with the clip, collecting lens on a stand, cardboard screen, graph paper, two guide rulers, measuring ruler, plate with three optical elements:

1. Fresnel mirror (square piece of foil with applied rings);
2. Glossy reflective stripe.
3. Plastic refractive element (orange piece of material covering the hole)

Turn on the laser only when you take measurements! The wavelength of the laser beam is $\lambda = 680\,\mathrm{nm}$.

Part 1. Lens

In this part of the problem the laser beam deflection angle from the optical axis should be considered small.

Place the lens on the stand between the guide rulers such that it could be moved in parallel to itself. Fix the laser in the tripod clip. Attach the cardboard screen to the laser. Direct the laser beam at the lens center such that the reflected beam is clearly visible on the screen. Ensure that the reflection is approximately backward. When the lens is displaced along the guide rulers the reflected spot moves across the screen. Note that the spot gets diffuse, that is why take measurements of the spot center.

1.1 For both surfaces of the lens, measure the dependence of the displacement $\Delta x$ of the reflected laser beam on the displacement $x$ of the lens. Plot graphs of the corresponding dependences.

1.2 Using the data obtained, determine the radii $R_1$ and $R_2$ of the two surfaces of the lens.

1.3 Place the screen at a certain distance $L$ behind the lens. Measure the dependence of the displacement $\Delta x$ of the refracted laser beam on the lens displacement $x$. Plot the corresponding graph.

1.4 Using the experimental data obtained, determine the focal length of the lens.

1.5 Calculate the refractive index $n$ of the lens material. Evaluate the experimental error of the refractive index.

Отговори

Решение

Оригинал в Архива: IZhO_2013_Exp_eng_fiz.doc