Optics is an important branch of general physics, and holography is a flourishing branch in optics, which uses coherent light interference to obtain all the information of objects.

The holographic photoreceptor is placed on the xy plane of z=0, and the photosensitive receives both the reference light and the spherical wave emitted from the object point, and is made into a holographic film after development processing.

It is necessary to make a proof here that the ± 1st order diffraction light behind the hologram forms the virtual image and the real image of the object point, and the position of the two image points is found.

Shen Qi takes into account the complex amplitude of the spherical wave in the plane of z=0, under the paraxial condition, that is, the center of the sphere is far enough away from the xy plane.

Here we get an approximation:

[（x-x0）^2+（y-y0）^2+z0^2]≈∣z0∣+（x-x0）^2+（y-y0）^2/2z0

When the holograms are illuminated with the original reference light, a round of mathematical processing is required to obtain the complex amplitude of the holograms.

……=βA^2Bexp{ik/2d0[（x-x0）^2+（y-y0）^2]}+……

This took Shen Qi a certain amount of time.

The truth is about to emerge, the first term to the right of the equal sign is the so-called "halo light" that basically propagates in the direction of the illuminated light, the second term represents a divergent spherical wave, and the third term is another order of diffracted light.

The key is the third term, which can be rewritten using the factor exp(-i4πux) using u=sinθ/λ and k=2π/λ.

Finally, Shen Qi completed the proof and obtained that the coordinates of the convergence point, that is, the real image point, were (x0-2d0 sinθ,y0,d0)

I entered the venue 10 minutes late, and finished the optical roll in 45 minutes, and Shen Qi checked it and handed it in.

Under the gaze of a group of sophomore brothers and sisters in the Academy, Shen Qi didn't stay too long, handed in the papers and left quickly.

In fact, Shen Qi was not the first person to hand in the paper, and there was a boy who turned in the paper earlier than him, about a few minutes earlier.

Shen Qi walked out of the classroom and found the first boy to hand in the paper standing by the window in the corridor.

The boy wears glasses, is quite tall, close to 1.9 meters, black clothes, black pants and black leather shoes, with his hands in his trouser pockets, standing straight, overlooking the not blue sky.

"This look, this temperament, at first glance, is a scholar, a fellow scholar. Shen Qi made a preliminary judgment on the boy.

Suddenly, the boy turned his head and glanced at Shen Qi and said, "I haven't seen you before." ”

Shen Qi: "My name is Shen Qi. ”

The boy nodded, saying hello, and continued to observe the haze-filled sky.

Shen Qi walked to the window, beside the boy in the courtyard, and watched the sky with the boy, and the visibility was very low.

The two of them just stood like this, without saying a word, and 3 minutes passed.

Shen Qi finally couldn't help it: "Senior brother, what did you see?"

The boy said: "Jupiter and Saturn are normal, but the trajectory of Uranus is abnormal. ”

Shen Qi replied quietly: "Uranus does not move along a precise ellipse, which can be explained by a dark force attracting it. ”

Boy: "Either way, Newton's laws are absolutely true within the solar system. ”

Shen Qi: "I agree with you, so Neptune was discovered. ”

A conversation between two Yan students actually revisits a classic case in the history of astronomy.

When it was discovered that Uranus did not orbit in an elliptical orbit, the laws of gravity were in danger of being overturned.

A physicist named Le Verrier boldly predicted that there must be a faint and invisible planet that was attracting Uranus.

Soon after, the planet was observed by the Berlin Observatory.

It is very beautiful with a pale blue body, and the earthlings named this blue planet after the Roman name of Aquaman Poseidon, "Neptune".

That's how Neptune was discovered.

Shen Qi is not good at astrophysics, but his teacher in the high school competition team is very good, Mu Rong is astronomy in his undergraduate science, and he was upgraded to astrophysics when he studied for a master's degree and a doctorate.

"Everything is consistent with Newton's law, the elliptic plane is not on the 'sky plane'. The boy said again.

"For longer distances, the law of gravity is also true. Shen Qi said.

"Yes, not only can we understand nebulae, but we can even get some inspiration from the laws of gravity. The boy said.

"What do you call Senior Brother?" Shen Qi couldn't take it anymore, this person is good at pretending to be B, I can't talk about him in the branch of astrophysics, I have to be my senior sister with a doctor of physics.

Yang Dingtian, major in astronomy. The boy gave a brief introduction to himself.

"Yang Ding Tianyang Sect Master?"

"Yang Liwei's Yang, people are determined to win the sky. ”

"Senior Brother Dingtian is a sophomore, right?"

"Sophomore. ”

"It's better to meet by chance, it's almost time for dinner, why don't we go have a drink or two? I believe you are a man with a story, and I, with wine. Shen Qi guessed that this style, this method of pretending to be B, Yang Dingtian must have a place on the list of the king of the academy.

Yang Dingtian: "No need, please go back." ”

Shen Qi was not annoyed: "It's okay, then I'll go back to the academy first, and come back another day to ask for advice." ”

"Are you from the Academy?" Yang Dingtian's calm face finally showed a hint of surprise.

"Freshman in the Department of Mathematics. Shen Qi discovered that his popularity in the Academy of Objects was not as high as he imagined, at least this Senior Brother Yang didn't know him.

"Freshman cross-major optics?" Yang Dingtian asked.

"I have a bachelor's degree in mathematics and am studying for a second degree in physics. Shen Qi told the truth.

"It seems that you are also a man with a story. Yang Dingtian couldn't help but look at Shen Qi a few more times, "Today's wine, I invite." ”

The two walked together towards the small restaurant outside the school.

"My past is very ordinary, I like mathematics and physics, and I came to Yanda in competitions. Shen Qi filled Yang Dingtian with a cup of snowflakes to brave the world, and then filled it for himself.

"IMO? or IPhO?" Yang Dingtian drank all the wine in his glass, and he was a bold man.

"IMO, what about you?" asked Shen Qi.

"My past is also very ordinary, IPhO. Yang Dingtian drank a cup and poured another glass, and added: "I have participated in two IPhO." ”

Shen Qi respected Yang Dingtian with a cup of glass, and drank the wine in one gulp: "Why did you choose astronomy?"

"Truth exists in the universe, and the vast majority of humanity is lost in oil, salt, sauce and vinegar. Yang Dingtian looked out the window and looked up at the sky, his eyes deep and firm.

"Senior brother's pattern is really grand. Shen Qixin said why don't you go to heaven, he added wine to himself: "Let's talk about some down-to-earth topics, which course is the most difficult in undergraduate physics?"

"It's okay, it's not that hard. Yang Dingtian said, "The difficulty of physics is not the technique, but the Tao, the Tao is natural, and everything changes from its origin." ”

"Brother Dingtian, let's be straightforward, what is the average score of your physics major class?" In the continuous exchange and exchange, human beings have made progress, and Shen Qi found from Yang Dingtian that the B system of the Institute of Physics is different from that of the Academy of Mathematics.