After a while, Eunuch Liu came back with a crystal rhino horn magnifying glass and some cut flowers.
Emperor Hongzhi smiled and asked the prince: "You also want to ask Mr. Cui to teach you the way of style? If you want to learn it, you must learn it with your heart, and you must understand the truth. If you are afraid of difficulties and act like a spoiled child, the master wants to scold you, and I will not. protect you."
Cui Xie glanced at the tray and turned his eyes slightly, as if he was about to talk about the Tao of Heaven and Man. The little prince's heart trembled, and he quickly shook his head: "I don't deserve this flower. It was brought by Liu Banban on his own initiative. I only need him to bring the crystal mirror."
How could this Liu Banpan not be so smart when he encounters matters related to Mr. Cui? In the early years, when my uncle forced him to make papers, he couldn't protect him; last time, when the uncles took away the servants in the East Palace, they couldn't think of an idea; this time, they took the wrong thing in front of the father and Mr. Almost got to hear some logic...
If I knew it earlier, I brought Tan Da Companion here.
The prince blamed him a little, so he stopped using him to fetch things, and turned back to Eunuch Gao: "My companion, bring me a few pieces of paper for Gu."
Eunuch Gao personally went to get a stack of jade plate paper, along with the pen and ink, inkstone, and pen wash, put the things away, and personally researched ink for the prince. The two father-in-laws next to the prince are younger than him, but they are not as neat as him.
In terms of their ability to serve people, how can these two people compare to Eunuch Gao, who survived Wang Zhi and Liang Fang, and became an eunuch of Sili's pen during the Chenghua period
Zhu Houzhao looked at Eunuch Gao's vigorous figure, and felt a little envious in his heart. But he didn't need a pen and ink, just walked over, took a piece of white paper and spread it in the sun, picked up a crystal lens and took a picture on the paper.
Cui Xie immediately understood what he was going to do, and immediately stopped him: "His Royal Highness wants to use this mirror to make fire? The Wenhua Palace is mostly decorated with wood and silk, which is easy to catch fire and does not cooperate with such a dangerous thing. The fire can be drawn on the stone bricks in the courtyard."
The prince deflected the lens, the light spots just gathered scattered into a piece, and said with a smile: "How could Gu set fire in the palace, I'm just curious, why this mirror was just removed from the paper when looking at things. , the bigger it is, the bigger it is, and it becomes blurry and invisible when it is far away? And when it is used to make fire, why does it have to be at such a high place so that it can gather the sunlight into small points, either up or down, then Is the aperture bigger?"
The back of Cui Xie's neck suddenly froze, and he glanced at the prince involuntarily - he managed to recall a little bit of high school biology, and he could confuse liberal arts students. Why didn't the prince ask about biology, but actually asked about physics
He only remembered that Zhu Houzhao didn't like reading and fighting, but he had never heard of this arrogant boy who liked to study physics!
The emperor on the jade steps only smiled and said "nonsense", and said warmly: "Mr. Cui will tell the prince, and I also want to hear what heaven is hidden in it."
Heavenly? What is the reason for the focusing of a convex lens... Is it the principle of refraction of light
Since the end of the sophomore exam, Cui Xie packed up the physics book and the formulas and theorems in his mind. Now that he is reminiscing, he only remembers that light will be refracted when it passes through a convex lens, and there is an inverted image or something, but if you want to explain it to others, it is impossible to explain.
He rubbed his heart like a washing machine, but his expression did not change at all, and even had an almost cold fortitude.
- What he doesn't understand, the prince and the emperor certainly don't understand. If it's a big deal, just measure data, draw pictures, and formulate calculations, and let the prince do the math twice by himself!
Cui Xie bowed his head and replied, "I don't dare to say I understand, I just have a few thoughts. If Your Majesty and the Crown Prince don't give up, I will tell you about the twists and turns of the sun shining through this lens."
The emperor nodded in agreement. He walked to the front of the case, took the magnifying glass from the prince's hand, and moved the position in the air until a tiny bright spot appeared on the paper. First, he named this point "Focus".
When the light converges to this point, it can burn the paper, so it is called the focus.
He couldn't remember how the focus in physics came from. Anyway, he had to introduce the word "focus", otherwise, how the light was refracted and focused in the back would be impossible to talk about.
It is not a new thing that the lens can be ignited, and the word "focus" is just as the name suggests. The emperor didn't care too much, and he hoped that he would talk about the way of yin and yang in depth.
The crown prince also seemed to understand, and asked him, "What does Mr. mean, the focus is only when the crystal mirror is just lifted so high, and it's not even higher and lower, so the paper can't be burned?"
Cui Xie smiled: "What the prince said is very true. At this time, measure how long the center of the lens is from the paper surface, and we call it the focal length of this crystal mirror. I have tried the crystal mirrors at home, and the thickness is different. Yes, the focal length is also different, you can ask your father-in-law to take a ruler to measure it."
Eunuch Gao immediately put down the pen and ink, Liu Jin reacted, and quickly said to the crown prince: "The slave and maid bring it for Lord Cui?"
The prince glanced at him and hesitated, but Cui Xie turned directly to the emperor and asked, "I still need a candle, two candlesticks, and a piece of thick cardboard, and then ask Lord Xie to help me with these things, so that I can be called Your Majesty. Face to face with the prince to see how the crystal mirror transmits light."
Crystal lenses naturally transmit light, why do they still use candlelight
The emperor was also a little curious like his son, and ordered the little servants on duty to get what he wanted. When the prince urged him to talk about the principle of focusing light again, Cui Xie asked him inexplicably to wait for the test, then stood quietly in front of the table, closed his eyes slightly, and recalled how to draw the refraction line of light in the image of the candle.
Forget it, draw as far as you can.
Anyway, the prince doesn't know as much as he does, so let's talk about it first. In the future, foreign countries will import optics books, and the prince has learned it. When he remembers that what he said is wrong, he will try his best to praise the prince's talent and admit that he was not good at the beginning of the matter, isn't it
Choi Xie's mentality is already very detached.
When the waiters brought the rulers and experimental utensils, he first measured the focal length, which was not very accurate, and then inserted one of the two candlesticks into the candle and the other with a magnifying glass, and placed it on the focal length according to the scale of the ruler. Xie Ying asked Xie Ying to support the large pair of cardboards, standing far away on the other side of the lens, and closed the doors and windows to do a convex lens imaging experiment.
At first, what was reflected on the cardboard through the lens was just a vague and scattered light and shadow. But when Cui Xie moved the candle a minute away, and Xie Ying also pushed the cardboard to the distance, at a certain position, a clear reflection of the candle flame like a mirror jumped out of the paper.
With an "ah", the prince pointed at the reflection of the candlelight in the center of the paper screen, and asked in surprise, "How could it be upside down! The crystals are so clear, the candlelight that passes through shouldn't be the same as the candlelight here. Is it?"
The Emperor couldn't help but move down to take a closer look, but Eunuch Gao rushed forward to serve and did not dare to leave.
The candle flame projected on the paper is larger than the real candle flame and is as clear as a reflection in a mirror. The royal family's most honorable father and son were both surprised and amused. They all looked at Cui Xie and asked him how this candle shadow became like this.
The experiment was successful, and the rest was just fooled. Cui Xie smiled calmly, and said to the emperor: "The appearance of the candle shadow is related to the convex and concave shape of the crystal mirror. Any light shining in from the focal distance we just mentioned can focus on the opposite side of the mirror. With such a shadow, let’s slowly push it out, note the length of the left and right, and the minister will explain it to His Majesty and His Royal Highness later—this length can actually be calculated.”
Emperor Hongzhi suddenly remembered the mysterious and mysterious feeling when he was talking about how to breed soybeans in front of the imperial court that day.
The emperor raised some precautions in his heart, and told him to move and measure, and as for how to calculate, he had the heart to teach the prince. He is now troubled by state affairs, not when he was in the East Palace, when he could ignore everything and only focus on the papers.
Emperor Hongzhi sighed secretly a few times, and then ordered the two to teach the prince a good life, and left Eunuch Gao to watch the teaching on his behalf. By the way, he arranged a banquet for the two heroes. He went back to the palace to read the memorial first.
The crown prince has no such experience yet. After sending off the royal father, he still concentrates on the candlestick. He also tried to push the candlestick out and the cardboard inward, and saw the clear candle shadows appearing on the paper screen again and again...
He didn't care too much either. Every time the candle shadow was clear, Cui Xie would write down a long and messy number.
Until the candle shadow on the cardboard was almost invisible, the crown prince was satisfied and had long forgotten what topic he wanted to toss Cui Xie with in the first place.
Mr. Cui is really a master of Confucianism. If examining things is so fun, he would be willing to examine them too!
The prince cleared his throat and wanted to send this set of things back to the East Palace, and then give some gifts to Teacher Cui and Assistant Teacher Xie. Unexpectedly, Cui Xie blew out the candle, so he asked people to reopen the doors and windows, and smiled at him: "Your Highness asked me about the heavenly principles hidden in this lens, and I would like to explain something to His Highness."
Oh... The prince straightened his body quickly and said respectfully, "Please explain, sir."
Mr. Cui took out the white paper and lightly drew a standard convex lens with the ink that Eunuch Gao had just developed.
When I was in school, I watched a geometry teacher draw a circle with freehand, and they all felt that they were very good at the bottom. Now that it was his turn to draw and teach, he realized that "there is no other, but he is familiar with it".
After painting embroidered portraits for so many years, now he can draw not only arcs with freehand, but also straight lines. The lines that run through the main optical axis of the picture, from the edge of the lens and through the center of the light, are as smooth and straight as those drawn on the boundary ruler.
He drew a scale of 1:10, put the focal length and double focal length on the optical axis, then took the two data just measured, and drew the imaging principle on the scale.
Zhu Houzhao looked at the dense lines and numbers, and for some reason, there was a little shadow in his heart.
However, Mr. Cui and Yan Yuese are all very simple. He has seen the phenomenon with his own eyes - as long as the candle is placed outside the focal distance, the reflection will be reflected on the other side of the lens. The closer you are, the smaller the image will be.
The little prince nodded frequently, feeling that he had fully understood the reason, but he turned his head to look at the distance between the lens and the candle on the table, and suddenly remembered something: "What if the candle is placed in the focal length, why can't it be imaged? ?"
Mr. Cui held the candle and the lens in front of him, and told him to look at the candle through the mirror—a magnified candle was reflected in the mirror, and the wax stains dripping from the candle were clearly visible.
The prince suddenly realized and let out an exclamation.
Cui Xie didn't want to talk about the principle of this virtual image, and he couldn't explain it very much. He simply kept the gentleman's good tradition of "calling a word and letting it understand itself", and he talked about something else with a smile: "We measured the focal length first, and placed the candle directly out of the focal distance when doing the experiment, so that it is easy to see the candle. In fact, if you change a different lens, you can also use the image size to reverse the image size without knowing where the focal length is…”
He extended the line running through the main optical axis and the edge of the lens on the picture, converged to a point, and then used that point as the vertex of the candle's reflection to draw a simple candle.
"Just ask people to measure the distance of the candle from the lens, the length of the candle flame, and the length of the flame reflected on the board, and the focal length can be calculated inversely."
He posed a few questions himself, drew pictures and calculated formulas for the prince in person. When I was drawing, I remembered a concave lens, and I drew a diagram of the refraction principle of a concave lens on the same optical axis.
After the drawing came out, he looked at the direction of the broken line, and his eyes suddenly lit up—
No wonder his tried-and-true microscope can make magnifications several times higher than ordinary magnifying glasses, but this telescope can't be done well. It is rare to see clearly, and the images seen are all upside down. , It turned out that he had the wrong lens in the first place!
Not two convex lenses, but one convex lens and one concave lens!
With the binoculars, the generals guarding the city on the nine sides will be able to detect enemy captives earlier and take precautions; in the future, when the Daming navy sails to the sea, he will also be able to set up a lookout on the mast to see if there are pirate ships or pirates in the distance. Island and reef!
He was so excited that his chest heaved slightly, and he almost forgot to teach the little prince a lesson. Fortunately, the prince looked a little dizzy and lost his mind when he saw these numbers, so he said to him: "I haven't learned much arithmetic yet, and some can't figure it out. How come Mr. Cui doesn't even need to memorize formulas, even if he comes up with such a long string of numbers. of?"
After asking the prince to ask this question, Cui Xie came back to his senses and looked at the numbers on the paper.
When he was in Guozijian, he also studied "Nine Chapters of Arithmetic", and most of it was fooled by the four arithmetic algorithms in elementary school, and he was not capable of teaching the prince to be a mathematician. Besides, the prince does not need to be a mathematician, as long as he has a little interest in mathematics, physics and chemistry, and is willing to accept modern science from foreign countries, it is enough for other ministers to help him understand.
Thinking of this, Cui Xie became more gentle, and taught the little prince a secret that was not shared: "His Royal Highness asked someone to surround it with a rope compared to the lines on the picture, and then measure it with a ruler, don't you know how long it is? If you want to know How big is the angle between this oblique line and the optical axis? It can also divide the sky into 360 degrees, and ask someone to make a semicircle protractor to measure it. Or go further, ask someone to calculate the slope of this line …”
There is no need for the prince to calculate by himself. He asked Xiao Huangmen to finish the calculation in advance and record the number. What the prince wants to calculate, can you know with a pair of digital watches? You don't even have to be right yourself, as long as you can think of an idea, the person who passes the calculation will just ask.
Unexpectedly, Mr. Cui is actually such Mr. Cui!
The prince was pleasantly surprised, and finally understood why the two uncles were punished by Mr. Cui for copying so many times, and now he is still mentioned in his favor.
If other gentlemen could allow him to memorize books, it would be great to find someone else to memorize them!
The Crown Prince was imagining with excitement, but Mr. Cui suddenly asked him: "The two father-in-laws beside His Highness are from the inner study, right? Since they are the people whom His Highness loves and trusts, you might as well ask them to learn a little bit so that it is convenient for His Highness to ask."
Gao Feng came from a serious inner study, a Hanlin disciple, but Liu Jin was not. He came up from a low-level eunuch. He could only say that he knew a few words and had read two books. He didn't understand the Four Books and Five Classics, and he knew nothing about arithmetic.
Usually, the prince only thinks that Liu Jin is considerate and able to serve, but he doesn't think he doesn't read. But when Cui Xie asked this question, he realized that Liu Jin knew nothing, was not as considerate as Eunuch Gao, his wife, and couldn't help him with his studies, so he couldn't take him out.
Eunuch Gao saw that the prince was a little hesitant, and said thoughtfully: "My little master intends to study the way of ethics, and there should be a few servants who can read to accompany him. The servant will tell the emperor, good emperor, Niangniang chooses a few good orders for the young master."