Imaging principle of small hole imaging

Principle: Light propagates in straight lines in the same homogeneous medium without being disturbed by gravity

The sun gives humans light and heat, which are indispensable to humans. light source. But due to the rotation of the earth, day and night are formed. Every night, darkness envelopes the land. Human ancestors living in ancient times were powerless against the night. Darkness gives people a scary and abominable feeling, and to this day darkness is still used by people to describe evil. It took countless centuries for humans to discover that fire could also provide light and heat. At first, natural fire was used, and later artificial friction was invented to make fire. The invention of artificial friction to make fire is an epoch-making progress in human history. It "allowed man to dominate a natural force for the first time, thus finally separating man from the animal kingdom." Peking Man, who lived half a million years ago, already knew how to use natural fire. About tens of thousands of years ago, humans learned to make artificial fire by drilling wood. Fire has been the only artificial light source available to people for a long time. Later, people created oil lamps and candles, but they were still inseparable from fire. It was not until the invention of modern light sources that they replaced fire.

Through long-term observation of light, people discovered that the light hitting the ground along the gaps between the leaves of the dense forest forms a ray-like beam, and the same is true for the sunlight entering the house from the small window. A large number of observational facts have led people to realize that light propagates in straight lines. In order to prove this property of light, about 2,450 years ago, the outstanding Chinese scientist Mo Zhai and his students conducted the world's first experiment in which a small hole formed an inverted image, and explained the principle of the small hole forming an inverted image. . Although he is not talking about imaging but shadowing, the principle is the same. A small hole is opened in the wall facing the sun in a dark room. When a person stands outside facing the hole, an upside-down figure appears on the opposite wall in the room. Why is there this strange phenomenon? The Mohists explained that light passing through a small hole travels in a straight line like an arrow. A person's head blocks the light above and forms a shadow below. A person's feet blocks the light below and forms a shadow above. This creates an inverted shadow. This was the first scientific explanation of the linear propagation of light.

The Mohists also used this characteristic of light to explain the relationship between objects and shadows. The shadow of a flying bird seems to be flying. Mohists analyzed the relationship between light, birds, and shadows, and revealed the secret that shadows themselves do not directly participate in movement. Mohists pointed out that the shadow of a bird is caused by the light traveling in a straight line hitting the bird and being blocked by the bird. When a bird is flying, the place where the light is blocked and a shadow appears at the previous moment is illuminated by the light at the next moment, and the shadow disappears; the new shadow that appears is formed by the light being blocked at the latter moment. Not a shadow of the previous moment. Therefore, the Mohists came to the conclusion that "the scene does not move", and the "scene" connects with the "shadow", that is to say, the shadow does not directly participate in the movement. So why does the shadow appear to be moving? This is because when the bird is flying, the shadow is continuously updated and changes position at the moment before and after. It seems that the shadow is flying with the bird. Mohists also explained the phenomena of projection and penumbra based on the principle of straight line propagation of light. In the mid-14th century, Zhao Youqin, an astronomical mathematician of the Yuan Dynasty, further examined the relationship between the image formed by sunlight passing through the pores in the wall and the pores in his "New Book of Gexiang". He found that when the pores are quite small, even though the shape of the pores is not circular, the images obtained are all circular (the principle involved is because: the small holes at this time image the image of the sun, so it is (circular); during a solar eclipse, the image is also missing, which is the same as the eclipse of the sun; the size of the hole is different, but the size of the image is the same, but the shade is different; if the image screen is moved closer to the small hole, the resulting image becomes smaller and brighter Increase. Regarding this phenomenon, Zhao Youqin came up with the rules of pinhole imaging after careful thinking and research. He believes that when the hole is quite small, no matter what the shape of the hole, the result is like an inverted image of the light source. At this time, the size of the hole is only related to the brightness of the image and does not change the shape of the image. When the hole is quite large, the resulting image is an upright image of the hole.

In order to confirm this conclusion, Zhao Youqin designed a relatively complete experiment. Dig two round wells with a diameter of more than four feet in each of the floors of the two houses downstairs. The well on the right is four feet deep and the well on the left is eight feet deep. Place a four-foot-high table in the left well, so that the two wells The depth is the same. Make two round plates with a diameter of four feet, and insert more than a thousand candles densely on each plate. After lighting them, place one at the bottom of the right well and the other on the table of the left well. Each cover at the wellhead is a round plate with a diameter of five feet and a small square hole in the center. The square hole on the left plate is about one inch wide, and the square hole on the right plate is about half an inch wide. At this time, you can see that all the round images appear on the floor, but the ones with larger holes are brighter and the ones with smaller holes are darker. Zhao Youqin used the principle of straight line propagation of light to explain that the candle in the east is imaged in the west, the candle in the west is imaged in the east, the candle in the south is imaged in the north, and the candle in the north is imaged in the south. Each candle has a corresponding image. Since there are more than a thousand candles, The candles are densely packed into a circle, and the images they form are also connected to each other to form a round image. This shows that when the distance between the light source, the aperture, and the image screen remains unchanged, the shape of the image remains unchanged, and there is only a difference in illumination: the one with a larger hole "accommodates more light" and is therefore brighter; Small ones "hold less light" and are therefore darker. If five hundred candles on the east side of the right well are extinguished, then half of the image on the floor of the right room on the west side will be missing, which is equivalent to the same shadow as the eclipse parts of the sun and the moon during a solar and lunar eclipse.

If the candles on the left are densely spaced and only twenty or thirty are lit, the image will be circular, but each of them is a dark square image that is not connected; if only one candle is lit, the square hole is not a candle light source. It is quite small, so the image of a square hole appears; if all the candles are relit, the image on the left will return to a round shape. Secondly, two large boards are hung on the floor parallel to the ground as image screens. At this time, the image screen is closer to the hole and the image seen becomes smaller and brighter. Then remove the two hanging boards mentioned above, still use the floor as the image screen, remove the table in the left well, and put the candle at the bottom of the well. At this time, the light source in the left well is far away from the square hole, and the image appears on the left floor. becomes smaller, and because the candlelight is weak, the brightness also becomes weaker as the distance increases. From these experimental results, Zhao Youqin summarized the rules of pinhole imaging and pointed out the relationship between the distance and intensity of the candle (light source) and the distance of the pinhole and image screen. He pointed out that when the image screen is close to the hole, the image is smaller. When the hole is far away, the image is large; when the candle is far away from the hole, it looks small, and when it is near the hole, it looks large; when the candle is small, it is bright, when it is large, it is dark; although the candle is close to the hole, the light is weak, and the image is dark; although the candle is far away hole, but the light is strong, the image will be bright. The last step of the experiment is to remove the two boards covering the well surface, and hang a round board with a diameter of more than one foot under the floor. The right board has a square hole four inches wide, and the left board has a triangular hole five inches long on each side. Adjusting the height of the plate is to change the distance between the light source, the hole, and the image screen. At this time, looking up at the image on the floor, there is a triangle on the left and a square on the right. This shows that the shape of the image formed when the hole is large is the same as the shape of the hole: if the hole is close to the screen, the image will be small and bright; if the hole is far from the screen, the image will be large and dim.

From the above experimental results, Zhao Youqin came to the conclusion that the image of the small hole is the same as the shape of the light source, and the image of the large hole is the same as the shape of the hole, and pointed out that this conclusion is "absolutely unquestionable." . Using such a rigorous experiment to prove the linear propagation of light and clarify the principle of pinhole imaging was unique in the world at that time.