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00:00:07
today's lesson we will devote to
00:00:10
determining the focal length of
00:00:13
collecting lenses experimentally from
00:00:15
installation you will have the same ones in
00:00:17
laboratory work in the sixth seventh
00:00:19
lessons so the topic of the lesson is the topic of
00:00:27
experimental determination
00:00:37
experimental determination of focal
00:00:43
length
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collecting and lenses
00:01:07
in this lesson we will look at how this is
00:01:10
done and in the next lesson you
00:01:13
do the laboratory work yourself,
00:01:17
determine the focal length, so
00:01:19
homework is to complete the laboratory
00:01:26
work for tomorrow,
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but now what is the first thing that comes to mind
00:01:34
when you decide to determine the focal
00:01:36
length of a converging lens, you and I know
00:01:38
that a converging lens allows you
00:01:40
to create a real image
00:01:41
of an object and we know the formula for a thin lens,
00:01:45
which means the first idea first thought
00:01:53
to use the thin lens formula:
00:01:57
one divided by the distance from the object
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to the lens
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plus one divided by the distance from the
00:02:06
lens to the image
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equals one divisor by the focal
00:02:10
length of the lens
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d is the distance from the object to the lens, but
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imagine that your lens has
00:02:21
this shape
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many collecting spectacle lenses have
00:02:29
such a shape where there are distances
00:02:33
where the optical center is, but that’s not so bad,
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you can assume that this lens is thin and
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somewhere here, and if the lens is
00:02:52
thick enough and by the way you will have to deal
00:02:55
with a rather thick one, here it’s
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no less than a centimeter relatively It’s
00:03:03
not clear why we should calculate these distances,
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so this method has very low
00:03:09
accuracy and we need to do something differently,
00:03:11
and now we’ll look at a
00:03:14
more advanced method, the one you’ll
00:03:16
use
00:03:17
today in laboratory work, for this
00:03:20
we’ll have to solve an auxiliary
00:03:22
problem and Goldfarb formulated before us,
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so we will solve the auxiliary problem
00:03:38
number twenty-six twenty-seven from
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Gald Farb,
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this can already be erased,
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let's get acquainted with the condition of the problem,
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here is 2627, let's move it
00:04:17
up a little like this and so the
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distance from the illuminated object to the
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screen is written here is 100 centimeters a lens placed
00:04:28
between them gives a clear image of an
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object on the screen in two positions, the
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distance between which is 20 centimeters,
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and so from the light source to the screen the
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distance is el large
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100 centimeters, and now the most important thing is
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a lens placed between them gives a clear
00:04:49
image on the screen in two
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positions, the
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distance between which is 20 centimeters
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gel small equals 20 centimeters
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we need to find the focal length, it’s
00:05:04
just ideal, the
00:05:07
problem from the problem book is adapted to our task, why is it better
00:05:14
than the task of determining the focal
00:05:17
length, which I described as the first
00:05:19
thought because we don’t need to know where the
00:05:23
optical center of the lens is,
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because we need to know to how much do you need
00:05:29
to move the lens in order for it to
00:05:31
create a sharp image
00:05:33
and why do you get two images
00:05:35
why do the lens have two positions
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Artem from the reversibility of light rays yes,
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but we don’t know how these images will differ
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until it comes to mind
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let’s see, we have a
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setup that we will use it
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now, I’ll show it, it’s big,
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here it is, we have a light source,
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a lens, and there you see an image, and
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what an object,
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and here’s an object, a small arrow, you see the
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image, which is enlarged, and now I
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’ll move the lens, the image became
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fuzzy, then nothing is visible at all, and
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then a tiny, reduced one image
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simple . even on a video camera it is not
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resolvable, but because it is too bright
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and the focusing of the lens is lost, but the
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eyes can be fixed, and so in the first
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case, the image is sharply enlarged and in the
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second case, the image is reduced, also
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sharp, and the distance by which you need to
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move the lens has
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nothing to do with the position of the
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optical lens center, so we
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won’t have any problems with this,
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we can determine this distance
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quite accurately, regardless of the
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thickness of the lens and what its shape,
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let’s then proceed to solve this
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problem, there are two positions, let’s
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depict both positions in the figure, here is the
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main optical axis in the first In this case, here is
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the main optical axis, in the second
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case, in both cases, we don’t
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move the object,
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here the object is the same, in the same
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place on our installation, this is this
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arrow, then here is the screen
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on our installation, here is the game, in the first
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case, we get a reduced
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image, well, for me on the contrary, in the first case
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we got an enlarged image, okay,
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let's show it here is the
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lens, the converging lens, that's how it
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is designated and we got an enlarged
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image, I won't build the details
00:08:33
of it, here it is in the second position, if you
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move the lens, it will be
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here, it will be here
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and the image will be reduced,
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but also clearly and here it is in both cases,
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really inverted, here it is
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enlarged, here it is reduced, you can
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build tricks, but we don’t need this now,
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we need something else, here is the distance from the
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object to the lens in the first case d1 here is the
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distance from the lens to the image in the
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second case f1 here the situation
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has changed here the distance from the object to
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the lens in the second case d 2 and here is the
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distance from the lens to the image in the
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second case f2 now what is given by the
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condition is the distance from the object to the screen
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it is indicated by the letter r large
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let's show it here here it is
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el large and it is also known that in
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order to get a clear 2 1 image,
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the lens must be moved at a distance of
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el small, this is the Elm distance,
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we will use the lens formula, for example,
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for this case,
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one on d1 plus one on f1
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equals one divisor by the focal
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length
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if we know d1 f1 we can from
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this formulas to express the focal
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length without problems, how can we find it
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if we instead of d1 f1 to at the distance
00:10:57
from the object to the screen and the distance by
00:11:00
which we need to move the lens, first
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of all, pay attention to this,
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according to the principle of reversibility of light
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rays that the order just mentioned,
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yes we can change in some places the image of
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the object in this case the distance that
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was previously the
00:11:19
distance from the lens to the image will
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now become the distance from the lens to
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the object therefore d2 and f1 we have
00:11:31
the same i d 2 equals f1 in the same
00:11:37
way f2 equals which the distance in the
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second case from the lens to the image is the same
00:11:46
as the distance in the first case
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from the lens to the object, that is, f 2
00:11:52
equals d 1 and now look, the
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usual geometry has gone, let's go from this
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position
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to this along this path,
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move first to d1 then noel and
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then to f2
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in total we will move at a distance
00:12:23
el large means we can write el
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large equals d1
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plus el small + f2
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but as we found out from the principle of
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reversibility of light rays f2 coincides
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with d1 in magnitude, which means plus d1 we can
00:12:45
find d1 from here since according to the conditions of the
00:12:47
problem el large and small
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we are given, we get it l equals
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2d one plus el small or 2d one
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equals el big minus film all and and
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here I will write d 1 equals than
00:13:09
el big minus and small in half is ready
00:13:19
now let's again go from this
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position to this in a
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different way so that we have
00:13:27
not d1a f1 was involved,
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look how you can do this, look
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at the second picture from this position we
00:13:39
move to d2
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and this is the same as f1 but we need to
00:13:43
get here moving here is not
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interesting let's go back to el malo and
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back and move to f1 again
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forward as a result we will move to
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el large means el large
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equals again look at el large
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equals f1 she is 2
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now back noel minus n and forward to
00:14:12
f1
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that is, we get l equals 2
00:14:20
f1 minus el mal and then
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2 f1 from here equals hotel big plus
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or small or I'll write it down here
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f1 equals look el big plus and
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small in half
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hoh we solved the most difficult part of the problem, we solved the most difficult part of the problem
00:14:48
through those quantities that are given according to the
00:14:51
condition we received those quantities that are
00:14:54
included in the lens formula, then it’s a matter of technology,
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this can be erased, we substitute the unit for
00:15:07
t1 and one on f1 here
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one on t1 reciprocal fraction 2 divided by
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p minus or plus one by f12 divided
00:15:23
by l + l equals the inverse focal
00:15:27
length what do you propose to do
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next what to do bring Andrey
00:15:35
correctly to a common denominator
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common denominator we will have a goal minus
00:15:41
n multiplied by n plus and here we will have
00:15:47
2 multiplied by an additional factor 2
00:15:50
multiplied by l + l add 2
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by this additional factor and
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minus or what is this inverse and focal
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length
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now open the brackets 2 el large
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this is the numerator of our fractions + 2 l
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small + 2n large -2 they don’t have enough
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x in the denominator that the difference of
00:16:33
squares is written or a large square minus or a
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little squared and all together it’s the
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opposite and the focal length is
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ready look at the numerator look
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here two with a plus here two with a minus
00:16:48
they cancel each other out
00:16:52
and it remains that two large plus 2 el
00:16:57
large this will be 4 large 4l large
00:17:03
divided by r square minus r square
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equals the inverse focal length
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but or optical power
00:17:11
but we are asked to find the focal length,
00:17:13
then we will reverse this freak and we
00:17:17
will get the focal length equals a
00:17:20
fraction in the numerator will be the difference of
00:17:24
squares in the denominator will be 40 large
00:17:35
here is our working formula since in the
00:17:39
conditions the numbers are given then the answer can be
00:17:42
obtained in the form of a number
00:17:44
we calculate f equals the fractional line in the
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denominator 4 l 4 per 100 centimeters in the
00:17:57
numerator the difference of squares you know it’s
00:17:59
probably easier to calculate using the formula
00:18:01
abbreviated multiplication the difference of
00:18:03
squares is n minus
00:18:04
el that is 100 minus 20 multiplied by n +
00:18:13
n 100 plus 20 centimeters square
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centimeters square centimeters are
00:18:19
partially reduced equal to the fraction
00:18:26
here we have 80
00:18:29
multiplied by 120 divided by 4 and on the table
00:18:36
let's do this once 2 we reduced a
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hundred times the denominator
00:18:41
1 2 we decreased a hundred times the numerator the
00:18:44
result is centimeters equals now 8
00:18:47
divided by 4 will be how much
00:18:49
2 2 multiplied by 12 24 the
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focal length of this lens is 24
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centimeters now we have done on the board
00:19:02
what you did in the laboratory work with your
00:19:05
own hands on a live
00:19:07
installation I will show you on this large
00:19:09
installation how we will work in what
00:19:11
sequence
00:19:13
and you will have this miniature one,
00:19:15
each of us has 9 of them,
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we are exactly 34 people, which means in
00:19:22
groups when we work there will be enough
00:19:24
for everyone and so we proceed to the actual
00:19:29
measurements for That’s probably why I
00:19:32
’ll now remove all the unnecessary stuff and organize a table
00:19:35
that needs to be filled out as we complete the
00:19:38
work. The only thing we need from this task is
00:19:40
this working form,
00:19:42
naturally, in the brief theory of the series I
00:19:45
wanted to ask about this before in the brief theory
00:19:49
you talk about how
00:19:52
this formula is obtained, necessarily because we
00:19:55
define the focal length, then in a
00:19:57
brief theory it will be necessary to describe what the
00:20:00
focal length is and list the
00:20:03
main elements of geometric optics,
00:20:07
that is, what is
00:20:08
the lens, the main optical axis, what is the
00:20:12
collecting lens, which
00:20:15
means that we will measure we
00:20:18
will set several distances from the
00:20:21
object to the screen which
00:20:24
We denote the letter l for several distances, that
00:20:27
is, we will have several experiments,
00:20:29
so the table will look something
00:20:31
like this:
00:20:37
experiment number You and I will now take two
00:20:45
measurements, in laboratory work you will
00:20:47
take 5 measurements 1 2 3 4 5
00:20:55
then we will change the
00:21:00
distances from object to the screen,
00:21:04
it is marked with us el large
00:21:08
centimeters further on the measuring
00:21:15
device on the optical bench, this
00:21:16
device is called an optical bench,
00:21:19
here there is a scale,
00:21:22
this scale allows you to determine the position
00:21:26
I or the coordinate of any object that is
00:21:31
located here, let's designate the two positions of
00:21:34
the lens on this scale as x 1, in
00:21:41
centimeters and
00:21:45
x2, in centimeters
00:21:50
means what it is these are the positions of the lens
00:21:54
at which a sharp
00:21:56
image is obtained, once enlarged
00:21:58
another time reduced, it
00:22:01
turns out that the countdown comes from here,
00:22:03
which means for an enlarged image
00:22:06
x1 will be a smaller value and for a
00:22:09
reduced image x1 will be a larger
00:22:11
value
00:22:12
therefore how to find the distance at which
00:22:14
we move the lens this was here the
00:22:19
coordinate x 1 became here the
00:22:21
coordinate x 2
00:22:22
must be subtracted, which means the next column l
00:22:28
is equal to x 1 minus x 2 centimeters,
00:22:35
in this formula we have everything
00:22:40
necessary to calculate the focal
00:22:42
length l we set x1 x2 we measure
00:22:47
here x1
00:22:50
by subtraction we find or it means we have
00:22:53
everything to calculate the focal length
00:22:56
we write f centimeters and take measurements
00:23:02
5 times
00:23:17
prepare this table for yourself now in your notebooks
00:23:21
and please tell me why I
00:23:23
left this column and
00:23:25
haven’t plundered it yet and and what do you think for the
00:23:28
average value f average centimeters
00:23:33
here our table ends with this is the
00:23:36
structure it has and you will need to take 5
00:23:40
measurements and fill in these five lines
00:23:44
calculate the focal length and find the
00:23:47
average value here is the table but
00:23:52
now let’s try to put into practice
00:23:54
what is planned so that you can clearly
00:24:00
see the camera, take a closer look, now we’ll
00:24:07
probably prepare a mouse so that I don’t run
00:24:09
to the computer all the time, now it
00:24:13
recognizes it,
00:24:14
now it recognizes the computer, let’s remove all the
00:24:18
unnecessary things,
00:24:25
now we can see either
00:24:31
everything in small plans or everything in close-
00:24:37
ups, pointing it towards the world, for example, at an
00:24:42
object
00:24:46
here now we need to determine where
00:24:49
the object is,
00:24:50
let's look at the scale, the position of
00:24:58
the object is against the number 5, which means the object
00:25:03
is at a point with coordinate 5,
00:25:05
let's set the distance from the object
00:25:08
to from to the image, that is, to the screen
00:25:11
70 centimeters, then we move along the
00:25:14
scale here and against 75 we set
00:25:22
the screen here this means that now the distance from
00:25:28
the object to the screen is 70 centimeters,
00:25:34
we write down l70 now the fun begins,
00:25:42
we need to build first an enlarged
00:25:45
image and then a reduced one,
00:25:50
we look at the screen,
00:26:01
I move the lens,
00:26:14
we make sure that the edges of the image
00:26:17
are as clear as possible,
00:26:20
we have built an enlarged image,
00:26:22
now we look at the position of the lens
00:26:27
here is the lens itself, here is the coordinate, let's say the
00:26:33
lens is how much 16.6 16.6 centimeters
00:26:45
we write down x1 16.6
00:26:52
now we move the lens so as to
00:26:56
get a sharp reduced image
00:27:11
look closely
00:27:13
it is very bright so we look where it
00:27:17
is and the lens itself the
00:27:28
position of the lens is
00:27:30
how much 60 2.1
00:27:35
is our x 2 62 and one tenth now
00:27:43
we take a calculator and subtract x we ​​even need
00:27:48
x 2 minus x1
00:27:50
from the larger the smaller you can put it here modulo
00:27:53
like this because it can
00:27:55
be the other way around for you if you put the screen on
00:27:58
the side where the smaller coordinate is the
00:28:01
opposite for you so that means 62 and 162
00:28:05
and one minus 16 and 6
00:28:10
it turns out 45 and a half 45.5
00:28:18
centimeters, and now the most exciting
00:28:21
moment is looking at this formula and using a
00:28:25
calculator we calculate the focal
00:28:28
length and so r-square I will immediately
00:28:33
calculate r in such large blocks
00:28:36
-square 70 squared minus
00:28:43
minus el small square here it is -45
00:28:48
and 5 squared is equal to what I did I
00:28:53
calculated the numerator now we need to
00:28:56
divide this result by 4 and also what we
00:29:00
get by dividing by el large
00:29:03
by 70 it turned out
00:29:15
just tell me please how many
00:29:21
significant ones I have the right to write down 3 digits
00:29:26
because we had length measurements with
00:29:28
three significant figures, which means three
00:29:31
significant figures it will be how much 10 point
00:29:34
one tenth 10 point one tenth
00:29:38
centimeter here is the focal length
00:29:42
further it’s too early to believe it
00:29:46
let’s change the distance between the
00:29:51
object and the screen it was 70 centimeters
00:29:54
let's do 50 for example like this oh Kolya
00:30:01
well done if it says centimeter here and
00:30:04
there is no need to write everything carefully,
00:30:05
look so now once again I remind you that
00:30:10
the object has a coordinate, that is,
00:30:13
its position is specified by the
00:30:15
five is at the position point of
00:30:18
which 5 centimeters the coordinate of the point is 5
00:30:21
centimeters we want to make it so that we
00:30:24
were at a distance of 50 centimeters,
00:30:27
so I move to a point 50
00:30:31
more, here it is 55 and here I place
00:30:38
the screen ready, record
00:30:46
50 centimeters and repeat the measurements
00:30:51
first you look and it’s a habit so first
00:31:01
we determine where the lens is when the
00:31:04
image is enlarged the screen must be
00:31:06
perpendicular to the main optical axis
00:31:09
we will fix let's move the lens like this,
00:31:14
let's let you see what's going on, I have the
00:31:18
camera in sight, so we'll move the
00:31:24
lens, turn on the mouse, retract,
00:31:38
move the lens,
00:31:42
here it is, a sharp image is ready,
00:31:51
measure the position of the lens at which
00:31:54
such a sharp image is
00:31:56
obtained, here's the lens, its position,
00:32:05
how many centimeters 18 3
00:32:12
x 118 and three centimeters, I’m no longer writing
00:32:19
now, please note that when we
00:32:23
moved the screen, the object had to be
00:32:26
moved a little from the lens to this
00:32:28
distance more than this, now
00:32:30
we move the lens so that we get a
00:32:33
reduced image,
00:32:38
it will be a little bit larger, so
00:32:43
we look where it is located where is
00:32:45
the lens at this position of the lens
00:32:53
what is 40.6
00:32:58
centimeters 40.6 centimeters we calculate the
00:33:05
distance by which we moved
00:33:07
the lens
00:33:08
means 46 -18 340. 6 minus 18 3
00:33:15
it turns out 22.3
00:33:22
now I use these values
00:33:24
el large and this value al
00:33:27
small we calculate the focal length and
00:33:30
so r-squared 50 squared well,
00:33:35
I’ll immediately write 2500 minus 22 and 3
00:33:40
squared 22 and 3 squared equals how much
00:33:45
then it turned out there now it needs to be
00:33:47
divided by 4 and by 50 but 4 by 50 is
00:33:53
200 means we divide by 200 let
00:34:00
’s see what happens what happens
00:34:11
10 point one hundredth
00:34:14
if you write down three significant figures and then it
00:34:18
will be that
00:34:20
10.0 class is a wonderful result
00:34:24
10.0 a why do I think that these are
00:34:29
wonderful results, yes, because
00:34:31
on this lens its focal
00:34:38
length is indicated as 100 millimeters, that is, 10
00:34:45
centimeters, see how well
00:34:47
this method works,
00:34:49
how accurate it is, although the lens is quite
00:34:51
thick, so it is impossible to obtain the position of the
00:34:55
optical center with great accuracy,
00:34:58
so using this method
00:35:01
you you will be in the sixth and seventh lessons in
00:35:03
groups doing laboratory work,
00:35:05
now I will give you the distances between the
00:35:11
object and the screen that you will
00:35:13
install as el large
00:35:17
el large equals 45 centimeters 40
00:35:25
centimeters thirty-five centimeters 30
00:35:31
centimeters and
00:35:33
25 centimeters that is, you will get five
00:35:37
lines, calculate focal length of another
00:35:40
lens there will be another five times you will find
00:35:44
the average this is the task we
00:35:47
face in lesson 2 now we are finishing the lesson
00:35:51
we are drinking tea

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Урок физики в Ришельевском лицее

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