Main Content

Eureka! Mexican solves physical problem with centuries without solution

“I remember that one morning I was preparing bread with Nutella, and suddenly I said: mothers! is there! “.

Narrates the Mexican Rafael González the right time when he discovered the solution to a problem optical physicist with centuries unresolved.

Isaac Newton himself could not solve it at the time and although approximations had already been found, no one had found the complete answer.

This is the solution to spherical aberration in optical lenses , with which now many industries (telescopes, cameras, etc.) can reduce large costs.

That morning, after months and months of trying to solve the equation that posed the problem, Rafael knew he already had it.

” I went up to my room, I started to program, I saw that he left and I started to jump with emotion,” he tells CONECTA.

Graduated from Tec de Monterrey of Industrial Physical Engineering , and currently pursuing a doctorate in nanotechnology right there, Rafael made an alliance with his friend Alejandro to solve the challenge.

Alejandro Chaparro, a graduate of UNAM, had invited Rafael to solve the problem; he had been looking for 3 years to solve it.

Both met in the master’s degree at the Optics Research Center.

I knew I was a mythical problem. There I met Alejandro;. I insisted and I invited us to solve the problem I would say it was a swamp and would not be able” , says Rafael.


The first to substantiate the problem was the Greek mathematician Diocles, more than 2,000 years ago.

Then, for centuries, scientists like Newton or Leibniz had tried to solve the challenge: to make the vision of objects through spherical lenses not lose sharpness.

Newton invented a telescope that solved the so-called chromatic aberration (which prevents focusing the colors at a single point), but not spherical aberration.

In the last century, in 1949, two scientists raised the dilemma in a formal article. From there, it would be known as the Wasserman - Wolf problem .

No one had been able to fully resolve it .

Newton or Leibniz had tried to solve the challenge: to make the vision of objects through spherical lenses not lose sharpness.


One solution for the problem was the conjunction of two lenses called not spherical but aspherical (only spherical in part of its surface).

However, until now, the calibration of these lenses depended on a not entirely accurate calculation.

(In contrast) the analytical solution (found by them) is accurate; using the equation you will have the precise result no matter what the variables change , ” he explains.

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

“We did very well because we had the distinction of the editor ; That is very rare: less than 1 percent of the 35 thousand articles have been published in that magazine have that distinction ” , account.

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


Julio César Gutiérrez, professor of Tec who advises Rafael on the doctorate , considered that having solved the problem may imply improvements in the development of lenses.

“Optical design has technological applications that involve optical systems. Then the results have relevance not only theoretically but in other applications.

“ Rafael is a very good student; Enthusiastic and independent. He has a lot of initiative to try to solve challenging problems. “


With 28 years of age, 6 articles published in scientific journals -4 of them on this subject- and 3 more in review, Rafael highlighted the support he received from Tec .

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

However, the greatest support I had from Tec was undoubtedly the confidence of my advisor, which drives you to propose something and share it, even if you get stuck,” he said.

And he testifies to that, being able to rest, having been able to solve this ancient problem.

He had been obsessed for many months now,” Rafael says laughing. But you can say: problem solved.”

Link to article