IOM 2019, Блиц — Задача 54

OLYMPIAD OF METROPOLISES, Moscow, September 2, 2019 · 2 септември 2019 г.

Условие

A polystyrene disk of radius $r = 14$ cm floats on the surface of the waterpool with a depth of $H = 2$ m. A lamp is placed above the center of the disc at a height of $h = 10$ cm. If we change the height of the lamp above the disc, we also change the size of the shadow at the bottom of the pool. What can be the maximum shade radius $R$? The refractive index of water is $n = 1.5$.

The answer should be given in the SI units unless otherwise stated. If the numerical result turns out to be an integer, it should be given as the answer. Otherwise round the result to the first decimal. $g = 10\ \mathrm{m/s^2}$.

Решение

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Оригинал в Архива: blitz-en-all-task-final.pdf