* “I remember** spreading Nutella on a slice of bread and suddenly saying, ‘Jeez! That’s it!’”.*

That’s how** Mexican ****Rafael González** describes the **precise moment** he **discovered the solution** to an optical physics **problem** that **hadn’t been solved for centuries.**

**Isaac Newton himself couldn’t solve it** in his day. Although there had been partial solutions, **no-one had found the complete answer.**

It was the solution to *spherical aberration*** in optical lenses**, which could now help **many industries** **make big savings** in producing items such as telescopes and cameras.

**That morning, after months and months of attempting to **solve the equation describing the problem,** Rafael knew he’d finally got it.**

**“***I went up to my room, began programming, saw the results and started jumping for joy”, *he told CONECTA.

Rafael is currently taking a **PhD in nanotechnology** at **Tec de Monterrey**, having also **graduated** from its **Industrial Physics Engineering program.** It was his friend Alejandro’s idea for them to team up to unravel the puzzle.

**Alejandro Chaparro, a UNAM graduate,** had** invited Rafael to solve the problem** after he’d been trying to solve it himself for three years.

The pair met while studying for their Master’s Degrees at the **Optical Research Center.**

*“I knew it was a legendary problem. **That’s where** I met Alejandro; he was insistent and kept asking me to help solve the problem. **I **told him it was a tough nut to crack and I wouldn’t be able to do it”**, *said Rafael.

**AN ANCIENT PROBLEM**

The **Greek mathematician Diocles** was the first person to pose the problem more than two thousand years ago.

Over the centuries since, scientists such as **Newton or Leibniz had taken a crack** at the **challenge, which is a loss of definition when viewing objects through spherical lenses.**

**Newton invented a telescope** that solved the problem of *chromatic aberration* (which prevents colors from being focused on the same point), but it didn’t solve *spherical aberration.*

**Two twentieth-century scientists formally expressed the problem** in an article in 1949. From then on, the problem would be known as the **Wasserman-Wolf problem.**

**No-one had been able to solve it **completely.

Newton or Leibniz had taken a crack at the challenge, which is a loss of definition when viewing objects through spherical lenses.

**THE SOLUTION AND GLOBAL RECOGNITION**

One solution to the problem was the **combination of two lenses that were not spherical but aspherical** (only spherical on part of their surface).

However,** until now, calibrating these lenses depended** on a **calculation that wasn’t completely accurate.**

*“(By contrast) the analytical solution (discovered by them) is exact; **by using the equation, you’ll get the **precise result**, regardless of a change in the variables”*, he explained.

“We calculated the efficiency of 500 rays, and the satisfaction average was 99.9999999999%.”.

Rafael and Alejandro **published the solution** in the article *General formula for bi-aspheric singlet lends design free of spherical aberration**,* in the journal *Applied Optics***.**

*“We were very fortunate, **because we earned the** Editor’s Pick**, which is very rare:** fewer than one percent of the 35,000 articles published in that journal **have that distinction”**, *he said.

*“In our study, **we calculated the efficiency of 500 rays, and the satisfaction average **for all examples** was 99.9999999999%.”.*

*Equation for solving the problem of spherical aberration in lenses.*

**THE FORMULA’S IMPACT**

**Julio César Gutiérrez, the Tec professor** who **is currently advising Rafael for his PhD**, considered that having solved the problem could imply **improvements in lens development.**

*“The optical design has **technological applications** involving optical systems. **So the results are not merely relevant in theory, but in other applications.*

*“Rafael is a very **good student. He’s enthusiastic and independent. **He has** a lot of initiative **for attempting to solve** challenging problems”.*

**SUPPORT FROM THE TEC**

At his **28 years** of age, **with 6 articles published in scientific journals** -4 of which are on this subject- and 3 more in review, Rafael** highlighted the support he had received from the Tec.**

He celebrated the **institution’s resources**, such as support with a Mathematica **software license**, which he used to prepare the equations and simulations for the problem.

*“However,** the biggest support I had from the Tec was undoubtedly my advisor’s confidence, which pushes you** to propose something and work your socks off, even though you get stuck”,* he said.

Rafael is proof of that, now that he can rest after having solved this ancient problem.

*“I’d been obsessed for many months”,* says Rafael with a smile on his face. But now he can say: **problem solved.**

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