Chapter 14 Appendix 1 Contributions of the Mohism to Science
The "Mojing" has eight articles on optics.It discusses the shadow problem, the pinhole imaging problem, the straight line problem of light, and the spherical mirror imaging problem. The records about optical experiments in Mojing all agree with the results of modern optical experiments.With just a few hundred words, a fairly complete and systematic optical work has been formed.Mr. Qian Zhaolin once said: "The earliest record of the world's optical knowledge is generally said to belong to Euclid. In his book there is a section of text that records light in a straight line... But no experiment can be found to prove it. ...The great discovery of the basic nature that is carried out in a straight line, the "Mojing" said that it came earlier than Euclid, and it came better. This is why the "Mojing" should have a lofty position in the history of world science ".For the above views, now sub-articles to illustrate:
"Jingxia": "The scene does not move, but it is said to be changing."
"Jing Shuo Xia": "Scenery, light until the scene dies, if it exists, it will last forever."
In ancient times, it was quite common to think that shadows do not move.The above "scenery" is the shadow.This article explains the theory that objects cover light and form shadows.As long as the object does not move, the shadow will not move either.This unmoving state is eternal cessation.So it is said that "if it exists, it will last forever".
As for the saying that the shadow is still there after the object is moved, it is just an illusion.There are similar statements in Chinese and foreign records.For example:
"Zhuangzi · Tianxia": "The scenery of flying birds is never moving. The arrowhead [zu family] is so fast that there are times when it can't stop."
"Liezi Zhongni":
Coincidentally, Zeno in ancient Greece also said that "a flying arrow does not move".There are similarities with the immovable shadow.It means that every point that the flying arrow passes has a certain position and is still. It cannot be at this point and not be at this point at the same time.So it doesn't move.
The above situation explains:
a An object blocks the sun and forms a shadow.Shadows are immobile.
b People sometimes think that shadows can move, which is an illusion caused by the continuation of the old shadow that has not disappeared and the new shadow that has been born.
c If the object moves and the sun shines on the original place, the shadow in the original place must disappear.
d If the object does not move, the original shadow does not move either.
"Jingxia":
"Jing Shuo Xia": "Scenery, two lights sandwich one light, and one light is the scene." It is clearly pointed out that a light source has only one shadow.Two light sources will have two shadows. (figure 1)
figure 1
Figure 1A, there is only one light source, and only one shadow is generated.Figure 1B is formed by the irradiation of two light sources A and B.That's why it is said that "speaking is important".If two light sources are symmetrically located on both sides of the tree, one side of the tree receives light A, and the other side receives light B, that is, each side has a backlight and one side receives light.Shadows are generated in the backlight.Two lights, two shadows.Another example is that there are strong light sources at the four corners of the football field, so everyone in the football field has four shadows.
The above instructions:
a An object can sometimes get two shadows because there are two light sources in two directions at the same time.
b If two light sources are symmetrically placed on both sides of the object, the object can only produce shadows on the side of the light.
"Jingxia": "When the scene arrives, it will be due at noon, and with the chief of the scene, it will be at the end."
"The next scriptures":
This section is about the theory that light can be imaged through a small hole and form a reflection. (figure 2)
figure 2
One of the keys to imaging is that the aperture (end) should be small.If the hole is too big, it won't be able to form an image.See Figure 3:
image 3
The light goes from right to left, the hole that passes through is too large, the light intersects at point A, and point A is in front of the screen, so it cannot be imaged on the screen.The size of the image is also related to the distance. (Figure 4)
The above instructions:
a The light passing through the small hole of the screen will be reflected on the screen.
b Luminous objects, reflective objects, and the distance between the screen and the screen determine the size of the reflection.
c Only when conditions are met can a reflection be formed on the screen.
"Jingxia": "Jing welcomes the sun, saying that he is fighting (should be turning)."
"Jing Shuo Xia": "Scenery, the light of the sun reflects people, and the scenery is between the sun and people."
If under normal circumstances, the light shines directly on the object, it should be as follows (Figure 5):
Figure 5
The sun shines from the left, and the back is on the right.
If there is a plane mirror to reflect and illuminate people, the following picture will be formed (Figure 6):
Figure 6
In the picture above (Figure 6), the sun shines on the flat mirror from the right.The light is reflected by the mirror, and then shines on the person, forming a human shadow, which is a special phenomenon between the sun and the person.So it is called "Jing Yingri", that is, "the light of the sun reflects the candle (shine) people". "Daylight anti-candle", that is, back light reflection.The reflection of sunlight is shown in the figure (Figure 7).
Figure 7
M is a plane mirror.Ray BA strikes point A and is immediately reflected as AD. CA is the vertical line. BAC is the entrance angle and DAC is the exit angle.This is the reflection of light.
"Jingxia": "The size of the scene is said to be in the ground (the ground should be 柂〔yiyi〕) (凵上干) far and near."
"The next scriptures":
This paragraph is about the shadow irradiated by sunlight. Its size is not only related to the distance, but also related to whether the object (wooden column) being illuminated is upright.If the column is upright, its shadow will be long; if the column is inclined, its shadow will be short.If the column is upright, its shadow will be lighter; if the column is inclined, its shadow will be thicker.Drawing description now (Figure 8):
Figure 8
In two diagrams A and B, the distance between the column and the curtain is equal, and the lengths of AB and A'B' are equal.Just because AB stands upright, the shadow is tall, thin, and light; A'B' stands obliquely, and the shadow is short, thick, and deep.
As for the distance of the column, it also affects the size of the shadow.Compare the following figure (Figure 9):
Figure 9
The candle is larger than the wood, and the candle is smaller than the wood, and the effect is not the same.Also compare the following figure (Figure 10):
Figure 10
"Jingxia":
"The next scriptures":
Within the center (focus), see Figure 11:
Figure 11
PQ concave mirror O spherical center F focus OX positive axis
AB, CD judge the virtual image formed by the real object A'B', C'D' A'B'>C'D'
If AB is close to the focal point, the experience will be greater and the shadow will be greater. If the CD is farther than the focal point, the image will be small and the shadow will be small.That is, A'B'>C'D'.But the resulting shadows are larger than the actual objects, that is, A'B'>AB, C'D'>CD.When the object is in the focus, the imaging must be behind the mirror, which is positive but virtual, and larger than the entity.That is to say, "one is big and right", that is, "starting from the middle, the edge is right and the length is straight".
Outside the center (focus), there are two situations:
a The object is located outside the center of the sphere, as shown in Figure 12:
Figure 12
AB is close to the center O of the sphere, so the image is large, and the shadow is also large, forming an image of A'B'. CD is far from the center of the sphere O, the mirror is small, the shadow is also small, and the image is C'D'. A' B' > C' D'.The images obtained are all smaller than the real objects and are inverted real images.This is "a small and easy".
b The object is located between the focal point and the center of the sphere, as shown in Figure 13.
Figure 13
AB is close to the focal point F, the image is large, and the shadow is also large, and the image is A'B'. CD is far away from the focal point F, the mirror is small, the shadow is also small, and the image is C'D'. A'B'>C'D'.The obtained images are larger than the real objects, A'B'>AB, C'D'>CD, which are inverted real images outside the center of the sphere.That is to say, "it fits in the middle and grows its straightness".
"Jingxia":
"Jing Shuo Xia": "Knowledge, the one who learns is close, the one who learns is great, and the scenery is also great; Qi (its) is far away, the one who learns is small, and the scenery is also small, but it must be correct."
There is only one image of a convex mirror.When the light body is moved closer to the mirror, the image is larger at the present light intensity; when the light body is moved farther away, the light becomes weaker, and the image is smaller.But they are all upright.
The imaging of a convex mirror can also be divided into two situations: one is when the object is far away from the mirror surface, a small and upright virtual image is generated behind the mirror; Upright virtual image.But the images are smaller than the real thing.
"Jingxia": "Standing in front of the mirror, the scenery will arrive. If there are many but few, it is said that it is in a few areas."
"The next scriptures":
Figure 14
PQ Convex mirror O Center of sphere F Focus point AB=CD A′B′, C′D′ are the small and positive virtual images of AB and CD behind the mirror, A′B′>C′D′
Regarding the imaging of plane mirrors, the original texts of "Jing Xia" and "Jing Shuo Xia" explain the following three situations:
a When an object looks down on a flat mirror, the image is single and upside down.
There is only one plane mirror imaging.The reason why it is an inverted image is because the shape, white and black, distance, and obliqueness of the image are all due to the appearance of the human eye when looking at the light (Figure 15).
Figure 15
PQ is a mirror. AB is a real thing. E is for eyes.
The light at point A hits point C on the mirror surface and is reflected to E; the light at point B strikes point D and is also reflected to E.And people only think that the reflected light is produced by reflecting from the R point of the mirror. R is the image point of A, similarly, S is the image point of B.In addition, each point on AB has image points, which are arranged in sequence as RS, and aggregated to form an object image. AF is the same length as FR. RS is an upside-down virtual image equal in size and opposite in direction to AB. The arrows of AB point upwards, and the arrows of RS point downwards, forming an inverted image.Because there is only one image, it is said that "there is a lack of scenery".
b Two flat mirrors form a 90° angle (Figure 16)
Figure 16
Two flat mirrors 0P and OQ, where OQ is placed flat on the table and OQ is leaning against the wall.The two mirrors form a 90° angle.Object A shines on the 0P and 0Q mirrors at the same time. E is for eyes.
According to the principle of reflection above, the virtual image of A on OP in Figure 16 is B, and the virtual image on OQ is C.The virtual image B becomes a virtual image D for the OQ mirror, and the virtual image C also becomes a virtual image D for the OP mirror, so there are three images in total.Because D is the coincidence of the two images, it is said that "Jiang Dang Jing Ju".
c The angle of the second flat mirror is less than 90°
If the angle between the two flat mirrors is less than 90°, there will be more than three images.The formula is: number of pixels=360÷angle-1.Assuming that the angle between the two mirrors is 12°, the number of images can be 360÷12-1=29.That is to say, the smaller the angle between the two flat mirrors, the more images will be formed.Now the following figure (Fig. 17) illustrates: A becomes a virtual image B on the flat mirror OP, B becomes a virtual image C on the flat mirror OQ, C becomes a virtual image D on the flat mirror OP again, and D becomes a virtual image F on the flat mirror OQ.In the same way, A becomes a virtual image G on the flat mirror OQ, G becomes a virtual image H on the flat mirror OP, H becomes a virtual image I on the flat mirror OQ, and I becomes a virtual image F on the flat mirror OP.So far, it coincides with the virtual image F of A on the OP mirror.A total of seven images are formed by the two mirrors, calculated according to the formula, 360÷45-1=7, the result is the same.In the above, because the imaging is repeatedly reflected, it is said "innumerable".
Figure 17
The flat mirror OP is connected with OQ. OQ is placed flat, OP is suspended, the angle between the two mirrors is ∠POQ, forming an angle of 45°, the object A shines on the second mirror, and E is the eye.
If the included angle is 120°, according to the formula, three images should be subtracted from one image, and two images should be obtained.Because the three images include a concrete image, but because it is no longer visible from the direction of the back of the mirror, it is said that "all use the north (back)".
"The smell of the scene" is followed by "the smell of the appraiser".After the object is imaged, it reflects one after another, so it is said "innumerable".Excessiveness is the opposite of normal, and here it means a positive angle. "It" is the same as "it". "body", part. "Being in the same place with all its body" is F in Figure 17, which is the superposition of two virtual images.
Notes:
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Notes: