вопросы на понимание

[avva]

В записи про ЕГЭ (это Единый Государственный Экзамен в России, для тех, кто не в курсе) yucca предложила "придумать вопросы по естественным наукам, которые проверяют не хорошую память на подробности, а правильную картину мира. Именно на уровне идеального выпускника школы, а не примитивные типа "Земля вращается вокруг Солнца или наоборот?""

Мой вариант:

* Ну времена года конечно опять-таки (т.е. отчего они меняются).

* Вывести формулу решения квадратного уравнения.

* Объяснить, как работает соломинка для питья (почему жидкость по ней поднимается, как происходит весь процесс).

* Объяснить, чем отличаются иррациональные числа от трансцендентных.

* Объяснить, почему ДНК - _двойная_ спираль, и как эта "двойственность" работает.

* Объяснить, почему 0.99999... и 1 - одно и то же число, и как это так странно получается.

* Почему чай быстрее остывает, если на него подуть?

Предлагайте ваши?

Comments

моя любимая, потому что моя

[flaass.livejournal.com]

Вы стоите в чистом поле и видите на небе радугу. Что вы видите в ее центре?

Re: моя любимая, потому что моя

[shkrobius.livejournal.com]

anything
http://www.polarimage.fi/phenom/newVP.htm

[flaass.livejournal.com]

Красиво. А по существу? Ответ-то знаете?

[shkrobius.livejournal.com]

Perhaps you mean the antisolar point, but the rainbows do not have centers; poor wording. BTW, there are situations when it is not the antisolar point. When?

[flaass.livejournal.com]

When it's solar.
> poor wording.
A good lawyer can make any wording poor.

А правильный ответ - "тень от своей головы".

[shkrobius.livejournal.com]

The shadow of the head IS the antisolar point.

No, it can't be solar. The answer is when the rainbow is above the sea (the reflected bow). Check
http://mysite.du.edu/~jcalvert/astro/bow.htm#Refl

PS: you cannot find better lawyers than kids at exams asked this type of questions. You will be answering what exactly do you mean by the center until you'll guide them all the way to the answer.

[flaass.livejournal.com]

> kids at exams asked this type of questions
Да и тут в комментариях их немало; например, про двойную спираль ДНК. Может, они и полезны, но off the point.
Кстати, термин "antisolar point" я раньше не встречал, спасибо!
"Тень от головы" все же лучше: потому что ее видно.

И еще один вопрос про радугу: почему она всегда такая размытая?

[shkrobius.livejournal.com]

Do you address it to me or suggest it for the kids at the exam?

[flaass.livejournal.com]

Not for ЕГЭ, obviously (as most of the questions asked here aren't). And not for you. But it might be interesting for some Avva's readers.

BTW I found two reasons.

[shkrobius.livejournal.com]

Diffraction and multiple scattering. In some bows the colors are sharply separated. One can give a long list of factors (any inhomogeneity translates into additional scatter) but it will boil down to these two factors. Diffraction is the main effect in the glories and silver linings, in most of the rainbows, too. The foggier it is, the more band overlap you get; sometimes even a white bow.

Your questions brought back sweet memories: my grandmother used Camille Flammarion's L'atmosphère and Hemri Fabre's La Vie des insectes to teach me French, as I proved resistant to the charms of Hugo. Ever since I felt very special about the rainbows, the beauty of the idea behind it. I think it is no accident that physics began with explaining the bow. The drive was theological in its essence: to understand the nature of the object chosen for the Noahian covenant (why is it the symbol of the endless future for us?) They began inquiring into it, and what do you know: along the way they invented science that became this promise of the endless future... Don't you think it is a clever trick to pull on us?

[flaass.livejournal.com]

Удивительно. Мои причины совсем другие:
1. У Солнца непрерывный спектр.
2. Угловой размер Солнца очень велик; аж пол-градуса.
Причем мне кажется, что основная - вторая.

[shkrobius.livejournal.com]

If you put a sunray through a glass prism you would see a nice spectrum that does not look smeared at all. So the continuum spectrum is not the problem. The problem is that, say, the red band is widened, by diffraction, so much that it blends with the the yellow, and becomes diffuse and fringy. You can make it so by spraying aerosol after the light emerges from the prism. That is common effect in rain curtains: there are small water/fog particles that diffract and scatter light in addition to the droplets that refract it. The angular size of the sun does not matter because for all practical reasons you can consider the sun rays parallel. This may seem counter-intuitive because the rays spread out through cloud openings, but this is a perspective illusion: the rays are parallel. It cannot be any other way due to the great distance to the sun and atmospheric scattering. The rainbow is formed by parallel sun beams rather than the sun disk viewed as a point source in the sky.

[flaass.livejournal.com]

> The angular size of the sun does not matter because for all practical reasons you can consider the sun rays parallel.

Yes, the rays from every single point of the sun to all droplets are parallel. This, in the first place, makes rainbows possible: you cannot see a rainbow from a spotlight you hold in your hand. But different points of the sun give you differently placed rainbows which sum up to form one fuzzy rainbow.

[shkrobius.livejournal.com]

You think of it as if the radiation comes only from the sun limb, i.e., if you have exclusively direct beam. But the radiation is global, and it includes the diffuse hemispherical radiation across the entire sky. As the latter comes from a much wider area, the global radiation is uniform and the sunrays can be considered parallel. What you say causes fuzziness does contribute to fuzziness in 22 deg haloes http://www.atoptics.co.uk/halo/circ1.htm
that you observe near the circumsolar sector.