Different Systems

Optics is an important branch of General Physics, Holography is a rapidly developing branch of optics that uses coherent light interference to obtain all the information about an object.

A holographic photosensitive film is placed on the xy plane with z=0. The film simultaneously receives reference light and spherical waves emitted from the object point. After development, a hologram is formed.

Here we need to prove that the ±1st order diffracted light behind the hologram forms a virtual image and a real image of the object point, respectively, and then determine the positions of the two image points.

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

Here we can obtain an approximate relationship:

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

When illuminating the hologram with the original reference light, a round of mathematical processing is required to obtain the complex amplitude behind the hologram.

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

This took Shen Qi some of his time.

The truth is about to come to light. The first term on the right side of the equation is the so-called "halo light," which propagates essentially along the direction of the illumination light. The second term represents a diverging spherical wave, and the third term is another order of diffraction light.

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

Finally, Shen Qi completed the proof, obtaining the coordinates of the convergence point, i. e., the real image point, as (x0-2d0 sinθ, y0, d0).

Arriving 10 minutes late, Shen Qi completed the optics test in 45 minutes, checked it once, and then handed it in.

Under the watchful eyes of a group of second-year students from the Physics Department, Shen Qi didn't linger, handed in his paper, and quickly left.

In fact, Shen Qi was not the first person to hand in his paper; another boy handed it in a few minutes earlier.

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

The boy wore glasses, was quite tall, nearly 1.9 meters, dressed in black clothes, black pants, and black leather shoes, stood ramrod straight with his hands in his pockets, gazing at the not-so-blue sky.

"Those eyes, that aura—he's clearly a top student, a kindred spirit," Shen Qi made his initial assessment of the boy.

Suddenly, the boy turned and glanced at Shen Qi, saying, "I haven't seen you before."

Shen Qi: "My name is Shen Qi."

The boy nodded, acknowledging the greeting, and then continued to observe the smog-covered sky.

Shen Qi walked to the window, next to the male student from the Physics Department, and looked at the sky with him. The visibility was extremely low.

The two stood there silently for three minutes.

Shen Qi finally couldn't hold back any longer. "Senior brother, what did you see?"

The boy said, "Jupiter and Saturn are normal, but Uranus's trajectory seems abnormal."

"You're looking at the stars in broad daylight?" Shen Qi replied calmly, "Uranus doesn't orbit along a precise ellipse; this can be explained by a dark force attracting it."

Boy: "Regardless, Newton's laws are absolutely correct within the Solar System."

Shen Qi: "I agree with your point of view, that's why Neptune was discovered."

A conversation between two Yenching University students actually revisited a classic case in the history of astronomy.

The discovery that Uranus does not orbit in an elliptical path raises the risk of overturning the laws of gravity.

A physicist named Le Verrier boldly predicted that there must exist a dark and invisible planet that is attracting Uranus.

Shortly thereafter, the planet was observed by the Berlin Observatory.

It is a pale blue planet, very beautiful, and Earthlings named this blue planet after Neptune, the Roman name for the sea god Poseidon.

That's how Neptune was discovered.

Shen Qi wasn't good at astrophysics, but his high school Physics Competition Team teacher was. Mu Rong majored in astronomy as an undergraduate and upgraded to astrophysics during her master's and doctoral studies.

"Everything is consistent with Newton's laws; the elliptical plane is not on the 'sky plane'," the boy added.

"The law of gravity also applies to even greater distances," Shen Qi said.

"Yes, we can not only understand nebulae, but also gain some inspiration from the laws of gravity regarding the origin of stars," the boy said.

"What should I call you, senior brother?" Shen Qi couldn't continue. This guy was such a show-off. He couldn't argue with him in the field of astrophysics. Only his senior sister, a PhD in physics, could do it.

"Yang Ding Tian, majoring in astronomy," the boy introduced himself briefly.

"Yang Dingtian, the leader of the Yang Cult?"

"Yang Liwei's 'Yang' signifies 'human determination to conquer nature'."

"Is Senior Brother Dingtian a sophomore?"

"Sophomore year."

"It's better to meet by chance than to invite someone. It's almost lunchtime, how about we go grab a couple of drinks? I believe you're a man with a story, and I have some wine." Shen Qi guessed that with this style and this pretentious manner, Yang Ding Tian must have a place on the list of the King of Show Offs in the Physics Department.

Yang Ding Tian: "No need, please leave."

Shen Qi wasn't annoyed. "Alright, I'll go back to the Mathematics Department first and come back to ask for your guidance another day."

"You're from the School of Mathematics?" A hint of surprise finally appeared on Yang Ding Tian's usually calm face.

"A freshman in the Mathematics Department." Shen Qi realized that his reputation in the Department of Physics was not as high as he had imagined; at least, this senior student, Yang, did not recognize him.

"You switched majors to study optics in your freshman year?" Yang Ding Tian asked.

"I've already received my bachelor's degree in the Mathematics Department and am currently pursuing a second degree in physics," Shen Qi revealed the truth.

"Looks like you're a man with a story to tell." Yang Ding Tian couldn't help but look Shen Qi up and down a few more times. "This drink is on me tonight."

The two walked together toward a small restaurant outside the school.

"My past was very ordinary. I liked math and physics. I was admitted to Peking University through a competition." Shen Qi filled Yang Ding Tian with Snow Beer and then filled his own glass as well.

"IMO? Or IPHo?" Yang Ding Tian downed his drink in one gulp, a truly hearty man.

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

"My past was quite ordinary, I've participated in two IPhOs." Yang Ding Tian finished one glass and poured himself another, adding, "I've participated in two IPhOs."

Being selected twice for the national physics team's six-person roster is quite impressive. Shen Qi Yang Ding Tian, downing his drink in one gulp. "Why did you choose astronomy?"

"Truth exists in the universe, but the vast majority of humanity is lost in the mundane details of daily life." Yang Ding Tian looked out the window, then up at the sky, his eyes deep and resolute.

"Senior's vision is indeed grand." Shen Qi thought to himself, "Why don't you just fly to the sky?" He poured himself more wine and said, "Let's talk about something more down-to-earth. Which physics course is the most difficult at the undergraduate level?"

"Fortunately, none of them are too difficult," Yang Ding Tian said. "The difficulty in physics lies not in the techniques, but in the principles. The principles follow nature, and all changes are rooted in the same fundamental principle."

"Brother Dingtian, just tell me straight, what's your average score in physics?" Through constant exchanges and discussions, humanity has made progress. Shen Qi discovered from Yang Ding Tian that the physics department's system of showing off is different from that of the mathematics department.