Pinhole imaging principle

Small hole imaging principle Small hole imaging observation If you eat a plate with a small hole between the screen and the object every day, the reflection of the object will be formed on the screen. We call this phenomenon pinhole imaging. Move the midplane back and forth, and the image size will change accordingly. This phenomenon reflects the essence of light propagation along a straight line.

[Edit this paragraph] Demonstration method

Put a sharp pencil and make a small hole in the center of a piece of hard paper. The diameter of this hole is about three millimeters. Try to stand it upright on the table. Then close the curtains and dim the light in the room.

Light a candle and put it near the hole. Take a piece of white paper and put it on the other side of the hole. In this way, you will see an inverted candle flame on the white paper. We call it the image of a candle. Move the white paper back and forth to see what happens to the image of the candle flame. The closer the white paper is to the aperture ratio, the smaller and brighter the image is; When the white paper slowly moves away from the small hole, the image becomes larger and the brightness becomes darker.

Change the size of the hole, and then we will observe what happens to the image of the candle.

You can punch holes of different sizes and shapes on the cardboard, and the distance between holes is several centimeters. At this time, on the white paper, several reflections corresponding to the holes appeared. The size is the same, but the definition is different. The bigger the hole, the less clear the image. As long as the hole is small enough, its shape, whether square, round or oblate, has no influence on the clarity and shape of the image.

experimental method

1. Put away candles, small hole screens and ground glass screens. Light the candle and adjust the height of the candle and the screen so that the center of the flame, the hole and the frosted glass screen of the candle are roughly in a straight line. The distance between the candle and the small hole screen should not be too large. After adjustment, you can see the real image of candle flame upside down on the ground glass screen.

2. Move the position of the candle or frosted glass screen, and you can see that the closer the candle is to the hole or the farther the frosted glass screen is from the hole, the larger the image will be.

The second type: cut off the top of the can, cover it with a plastic film and drill a small hole in the bottom of the can. The inverted image can be obtained on the plastic film by pointing the small hole outward to the luminous object.

[Edit this paragraph] Explanation of the problem

This experiment raises at least three questions for us: Why is the image of a small hole upside down? What factors are related to the size of the image? What factors are related to the clarity of the image?

In order to explain these problems, we regard the flame of a candle as composed of many small luminous points, each of which radiates light in all directions. There will always be a small beam of light going straight through the hole and forming a small spot on the white paper. Each luminous point on the candle flame will form a corresponding light spot on the white paper, and all the light spots on the white paper will form the image of the candle flame.

As can be seen from the picture, the light from the upper part of the candle flame passes through the small hole straight and shines on the lower part of the white paper; The light from the lower part of the candle flame shines on the upper part of the white paper through the small hole, so a reflection is formed on the white paper. This just shows that light travels in a straight line.

As shown in the left picture, when the holes are small, the light emitted from different parts of the object also reaches different parts of the image, so the light emitted from different parts of the object will not overlap, so the image will be clearer. For example, the light emitted by object C will not reach B, so the light emitted by object C will not overlap with the light emitted by object A, so the image at B will be clearer. Once the hole is large enough, the light from different parts of the object will overlap at the image, and the image will be unclear. For example, the light emitted by part C of an object will overlap the light emitted by part A of the object in part B, so that the image of part B will not know whose image it is, and the natural image will not be clear. So the plate and the hole are equivalent to a resolver, which decomposes the light from different parts of the object, so it is imaged. In our daily life, we can't see the image on a piece of white paper facing the object, not because there is no light from the object on the white paper, but because the light from different parts of the object overlaps on the white paper, so our eyes can't see the image of the object. Once we project the light from the object onto different parts of the white paper with a lens or a small hole, the image of the object appears. Of course, the size is relative, and the size of this hole is relative to the object's big novel. If the object is large, then the hole is relatively large and can still be imaged. Only the smaller the hole, the higher the resolution of the image. Of course, if the hole is too small, there will be less light passing through and the image may not have enough brightness. Moreover, too small aperture will produce diffraction, which will also have an impact on imaging.

The size of the hole is relative. In fact, the size of the pinhole imaging hole is related to the object. If the object is big, the hole can be big, and if the object is small, the hole must be small. If we want to be the image of the sun, it is not impossible to use a hole as big as a football field. Of course, there is the problem of the distance between the screen and the hole. If the size of the hole is fixed and the distance between the hole and the object is fixed, the farther the screen is from the hole, the higher the theoretical resolution of the image is. Of course, in this case, the limit of resolution is the size of the hole, which means that the details smaller than the hole on the imaged object cannot be clearly distinguished. If we use a hole as big as a football field to image the sun, then the structure smaller than a football field on the sun will not be imaged.

If we use φ to represent the smallest structure of a distinguishable object, while U represents the object distance, V represents the distance from the screen to the pinhole (image distance), and φ represents the diameter of the pinhole.

The imaging formula is:

φ/φ=(u+v)/v( 1)

After finishing (1), we can get:

φ/φ- 1 = u/v(2)

As can be seen from formula (2),

When U and φ are fixed, and V tends to infinity, φ/φ tends to 1, so the image will reach the maximum resolution only when the image distance is infinite. The smaller the v, the lower the resolution. When v approaches zero, the image cannot be imaged and becomes a persistent spot.

[Edit this paragraph] Ancient stories

More than two thousand years ago, China scholar Han Fei recorded an interesting story in his book: someone asked a painter to draw a picture for him. Three years later, the painter told him, "It's done!" As soon as he saw that there was only one layer of paint on the eight-foot long board, there was no painting, so he lost his temper and thought that the painter had cheated him. The painter said, "please build a house with a high wall, and then open a big window on the wall opposite this wall." Put the blackboard on the window. As soon as the sun comes out, you can see a picture on the opposite wall. " He did what the painter said with a grain of salt. Sure enough, on the wall of the house, images of pavilions and chariots and horses appeared, just like a colorful landscape painting. What is particularly strange is that the people and cars in the painting are still moving, but they are all upside down!

About 24,500 years ago, China scholars-Mo Zhai and his students-made the world's first experiment in which small holes became inverted images, explained the reasons why small holes became inverted images, and pointed out the essence of direct light. This is the first scientific explanation for the straight-line propagation of light. In Mohist classics, pinhole imaging is recorded as follows:

"Book scene, in the afternoon, book scene. Let's talk about it at last. "

"Scene. People with light, if they shine, the people below are also tall; The tallest person will also go down. The feet cover the lights, so the scenery is at the top; The first cover is glazed, so it becomes a scene. There is an end in the distance and light, so it is also in the scene library. "

The word "inverted" here means "inverted", which means inverted. "Noon" means that two beams of light cross in the middle. "Duan" means "pole" and "micro point" in ancient Chinese. "Noon end" refers to the intersection of light, which is the pinhole. The reason why the projection of an object has an inverted image is that light travels in a straight line, and at the pinhole, beams from different directions cross each other to form reflections. According to the relationship between the position of the pointer hole and the projection size. "A bright man shines brightly" is a vivid metaphor. "Warmth" is the light that shines on people, just like archery. "The lower is also high;" The tallest person goes down "means that the light shining on the upper part of the person is imaged on the lower part;" The light shining on the lower part of a person is imaged on the upper part of the person. Therefore, when an upright person is imaged through a pinhole, the projection becomes inverted. "Library" means that the inside of the cassette has an end, and light "points out the relationship between the light and shadow reflected by the object and the pinhole distance. The farther away the object is, the smaller the image is; The closer the object is, the bigger the image is.

Mo Jing's description of pinhole imaging more than two thousand years ago is exactly the same as that of photographic optics today.

[Edit this paragraph] Imaging principle

Principle: Light travels in a straight line in the same uniform medium without the interference of gravity.

The sun gives light and heat to human beings and is an indispensable light source for human beings. But due to the rotation of the earth, day and night are formed. Every night, darkness covers the earth. The human ancestors who lived in ancient times could do nothing about the night. Darkness gives people a terrible and hateful feeling, and it is still used to describe evil today. I don't know how many centuries passed before man discovered that fire can also provide light and heat. Natural fire was used at first, and then artificial friction was invented to make a fire. The invention of artificial friction fire is an epoch-making progress in human history, "making people dominate a natural force for the first time, thus finally separating people from the animal kingdom." Peking man who lived 500,000 years ago already knew how to use natural fire, and about tens of thousands of years ago, human beings learned to make artificial fire by drilling wood. For a long time, fire has been the only artificial light source that people can use. Later, people created oil lamps and candles, but they still couldn't do without firing. It was not until the invention of modern light sources that fire was replaced.

Through long-term observation of light, it is found that the light shining on the ground along the gaps between leaves in dense forests forms a ray-like beam, as does the sunlight entering the house through small windows. A large number of observation facts make people realize that light travels along a straight line. In order to prove this property of light, about 24,500 years ago, Mo Zhai, an outstanding scientist in China, and his students made the world's first experiment of turning a small hole into an inverted image and explained the principle of inverted image. Although what he said is not imaging but forming shadows, the reason is the same.

A small hole was opened in the Chaoyang wall of a dark hut. People stood outside the house facing the hole, and an inverted figure appeared on the wall opposite the room. Why is there such a strange phenomenon? Mohism explained that light travels in a straight line through a small hole, like archery. People's heads cover the light above, forming a shadow below, and people's feet cover the light below, forming an upside-down shadow. This is the first scientific explanation for the straight-line propagation of light.

Mohism also uses this characteristic of light to explain the relationship between objects and shadows. A flying bird, its shadow seems to be flying. Mohist school analyzed the relationship between light, bird and shadow, and revealed the secret that shadow itself did not directly participate in sports. Mohism pointed out that the formation of bird shadow is because the light traveling in a straight line shines on the bird and is covered by the bird. When the bird is flying, the place where the shadow appears is covered by light one moment, and the shadow disappears when it is illuminated by light the next; The new shadow is formed when the light is blocked in the next moment, not the shadow of the previous moment. Therefore, Mohist school draws the conclusion that "the scenery does not move", and "the scenery" and "the shadow" are interlinked, that is to say, the shadow does not directly participate in the movement. So why does the shadow seem to be moving? This is because when the bird is flying, the shadow is constantly updated back and forth and changes its position. It seems that shadows are flying with birds. Before 24,500 years ago, it was really valuable to study the nature of light in this way and explain the relationship between moving and immovable shadows. Mohism also explains the phenomenon of projection and penumbra from the principle of straight-line propagation of light.

/kloc-In the mid-4th century, Zhao Youqin, an astronomical mathematician in the Yuan Dynasty, further investigated the relationship between the image formed by sunlight passing through a hole in the wall and the hole in his book "A New Record of Pixiang". He found that when the pores are quite small, even if the shape of the pores is not round, the resulting image is round; During the solar eclipse, the image is also missing, just like the solar eclipse; The size of the hole is different, but the size of the image is equal, but the shade is different; If you move the image screen closer to the small hole, the obtained image will become smaller and the brightness will increase. For this phenomenon, after careful thinking and research, Zhao Youqin came to the pinhole imaging law. He thinks that when the hole is quite small, no matter what the shape of the hole is, it is like the reflection 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 small hole is imaged schematically. Sometimes, the obtained 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 on the floors of two families downstairs. The well on the right is four feet deep and the well on the left is eight feet deep. Put a four-foot table in the left well, so that the depth of the two wells is the same. Make two circular plates with a diameter of four feet, and insert 1000 candles into each plate. After lighting, put one on the bottom of the right well and the other on the left well platform. The wellhead is covered with a round plate with a square hole in the middle and a diameter of five feet. The square hole of the left disk is about one inch wide, and the square hole of the right disk is about half an inch wide. At this time, you can see that the images on the floor are all round, but the big holes are brighter and the small holes are darker. Zhao Youqin explained that oriental candles are imaged in the west, western candles are imaged in the east, southern candles are imaged in the north, and northern candles are imaged in the south. Every candle has a corresponding image. Because more than 1000 candles are densely round, the images formed are also connected with each other to form a round image. This shows that under the condition that the distance between the light source, aperture and image screen is constant, the shape of the image is unchanged, but the illumination is different: the aperture is large, "containing more light", so it is brighter; Small holes "contain less light", so they are dark. If you light 500 candles on the east side of the right well, the image on the floor of the right room will be less than half in the west, which is equivalent to the eclipse when the shadow is equal to the eclipse. If the candle on the left is mixed with sulfhydryl, only 20 or 30 candles are lit, and the image is round, but each candle is a dim square image that is not connected; If only one candle is lit, the square hole is not small for the candle light source, so the image of the square hole appears; Re-light all the candles, and the image on the left will be round. Secondly, two large boards are hung on the floor parallel to the ground as image screens. At this time, the image screen is close to the hole, and the image you see 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 of the left well is far away from the square hole, and the image of the left building becomes smaller, and the brightness becomes weaker after the distance increases due to the weak candlelight. From these experimental results, Zhao Youqin summed up the law of pinhole imaging, pointed out the relationship between the distance and intensity of candle (light source) and the distance between pinhole and image screen, and pointed out that the image screen is small near the hole and large when it is far from the hole; Candles look small far from the hole and big near the hole; Small to light, big to dark; Although the candle is close to the hole, the light is weak, like dark; Although the candle is far from the hole, the light intensity and image are very bright. The last step of the experiment is to remove the two plates covering the well surface and hang a circular plate with a diameter of more than one foot under the floor. The right plate has a square hole four inches wide and the left plate has a triangular hole five inches long. Adjust the height and bottom of the board to change the distance between the light source, the hole and the image screen. At this time, look up at the image on the floor, there is a triangle on the left and a square on the right. This shows that the image formed when the hole is large is the same as the shape of the hole: the hole is close to the screen, and the image is small and bright; This hole is far away from the screen, like a big dark hole.

From the above experimental results, Zhao Youqin came to the conclusion that the image of the small hole is the same as that of the light source, and the image of the large hole is the same as that of the hole, and pointed out that this conclusion is "beyond doubt". It was unique in the world at that time to prove the linear propagation of light and clarify the principle of pinhole imaging with such rigorous experiments.

[Edit this paragraph] Property application

The linear propagation of light has been widely used in ancient astronomical calendars in China. Our ancestors made standard watches and sundials and measured the length and direction of shadows to determine the time, winter solstice and summer solstice. Install peepholes on astronomical instruments to observe the sky and measure the positions of stars.

In addition, our country has long used this characteristic of light to invent shadow play. In the early Han Dynasty, people and things cut by Qi Shaoweng were performed behind a white screen, and the images of people and things were reflected on the white screen with light, so people outside the screen could see the performance of the images. Shadow play was very popular in the Song Dynasty, and later spread to the West, causing a sensation.

Nowadays, some cameras and video cameras use the principle of pinhole imaging-the lens is pinhole (most of them are equipped with convex lenses to ensure the imaging distance of light), the scene enters the darkroom through pinhole, and the image is left on the film by some special chemicals (such as developer) (digital cameras and video cameras store the image in the memory card through some photosensitive elements).

[Edit this paragraph] Related tests

Purpose and requirements

Understand the law of pinhole imaging and the one-to-one correspondence between object points and image points.

Instruments and equipment

Candle, small hole screen (aperture 1-3mm), frosted glass screen.

experimental method

1. As shown in Figure 2.2- 1 Place candles, small hole screens and ground glass screens. Light the candle and adjust the height of the candle and the screen so that the center of the flame, the hole and the frosted glass screen of the candle are roughly in a straight line. The distance between the candle and the small hole screen should not be too large. After adjustment, you can see the real image of candle flame upside down on the ground glass screen.

2. Move the position of the candle or frosted glass screen, and you can see that the closer the candle is to the hole or the farther the frosted glass screen is from the hole, the larger the image will be.

Matters needing attention

1. With the demonstration, to draw the optical path diagram of pinhole imaging, the linear propagation law of light should be used to explain that pinhole becomes an inverted real image and the one-to-one correspondence between object points and image points.

2. The size of the hole and the distance between the object and the hole should be appropriate to ensure that the real image is clear and has a certain brightness. Generally speaking, the smaller the aperture, the clearer the image and the worse the brightness of the image; The larger the aperture, the greater the distance between the object and the pinhole screen.

3. The rough surface of the frosted glass screen corresponds to the small holes, so the observer can see the real image from the diffuse reflection of light from the rough surface of the screen or the light transmitted from the frosted glass screen.

This experiment should be done in a dark room.

reference data

The pattern shown in Figure 2.2-2 is composed of several small light bulbs, and it is used as an object screen to do pinhole imaging experiments instead of candles.

Arrange the object screen, pinhole screen and ground glass screen as shown in Figure 2.2-3, so that their centers are roughly in a straight line. Light up the small light bulbs on the object screen in turn. For example, starting from the light bulb at the end of the arrow, you can see small circular light spots appear on the ground glass screen in turn until a pattern similar to the object appears on the screen. This experiment can intuitively see the one-to-one correspondence between object points and image points. The aperture of the small hole used in the experiment can be larger to increase the brightness of the image.