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J. Perelman
"Entertaining physics". Book 2.
Chapter 9. Reflection and refraction of light. Vision

HOW MUCH WE THINK THE MOON?

By the way - about the apparent size of the moon. If you will ask friends, what size is the Moon, you will get a variety of answers. Most will say that the Moon is the size of the plate, but there will be those, which it seems to be the size of saucers for jam, cherry, Apple. One pupil Moon always seemed to be the size of a round table on twelve persons". As one writer claims that the sky was the Moon diameter of a yardstick.

Why such difference in views about the value of one and the same subject?

It depends on differences in the value of the distance - estimation is always unconscious. The person seeing the moon the size of an Apple, is her at a distance much less than those people who it seems with a plate or round table.

Most people, however, imagine the moon the size of a plate. From this we can draw an interesting conclusion: If we compute (the calculation method will become clear from the further), what distance puts each of us the moon, which has the same apparent size, it appears that the deletion does not exceed 30 PM Here on what modest distance we unconsciously pushing our night light!

On an erroneous estimate distances based not enough illusions of view. I remember an optical illusion which I experienced in early childhood, "when I were new all the impressions of life." A native of the city, I once in the spring, during the outing, the first time in my life I saw grazing in the meadow the cow herd, as I misjudged the distance, cows, these seemed like a dwarf! Such tiny cows since then I have never seen and, of course, will never see*.

The apparent size of the stars astronomers determine the magnitude of the angle under which we see them. "Angular size", "angle" is the angle, which is made up of two straight, held to the eye from the extreme points of the body (see figure). Angles, as is known, measured in degrees, minutes and seconds. On the question of the apparent size of the lunar disk astronomer will tell you that the disc is Apple or a plate, and will answer that it is equal to half degrees; this means that straight lines drawn from the edges of the disc to our eye, make the angle of half a degree. This definition of visible size is the only correct one, does not generate confusion.


What is the angle of view.

Geometry teaches that the object remote from the eye at a distance of 57 times larger its diameter, must be submitted to the observer at an angle of 1 degree. For example, Apple 5 cm in diameter will have an angular size of 1 degree, if it is to keep an eye on the distance I see At a distance of twice the larger it will appear under an angle of 0.5 degrees, i.e., the same value which we see the moon, If you like, you can say that the Moon seems to you the size of an Apple, but provided that the Apple is removed from the eye at 570 cm (about 6 m). If you wish to compare the apparent size of the moon with a plate you have to move the dish for about 30 meters. Most people don't want to believe that the Moon seems so small; but try to put a dime at a distance from the eye, which is 114 times greater than its diameter: he will cover the moon, although removed from the eyes of two meters.

If you were asked to draw on the paper circle representing the disk of the moon, visible to the naked eye, the task would seem you are not certain: the circle can be both big and small, depending on how far he is removed from the eye. But the conditions will be determined if you focus on the distance at which we usually keep books, drawings, etc., i.e. at a distance the best view. It is for the normal eye 25 see

Now, let's calculate what the values should be in the circle at least on the page of this book, to the apparent size was equal to the lunar disc. The calculation is simple: we have to divide the distance of 25 cm to 114. Will get a very small amount - a little more than 2 mm! Approximately the width of the letter "o" printed in the font of this book. I can't believe that the Moon, as well as equal to her apparent size of the Sun seem to us at such a small angle!

Did you ever notice, it is likely that once your eyes have been aimed at the Sun, in the field of view, long flashing colored mugs. These so-called "optical traces have the same angular size as the Sun. But the apparent size change: when you look at the sky, they are the size of the solar disk; when I look in front of you lies a book, "trace" of the Sun is on the page, place a circle with a diameter of about 2 mm, clearly confirming the correctness of our calculation.

* However, adults sometimes amenable to such illusions. This is evidenced by the following passage from the story Grigorovich "Plowman". "At opened at a glance, the village seemed beside the bridge, the house, the hill and birch copse seemed now adjacent to the village. All this - and the house and garden, and the village took now those toys where the stems of moss depict trees, pieces of mirror - river".

Entertaining physics J. Perelman

 




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