This is a fascinating question that delves into the very nature of light and how it interacts with other electromagnetic fields. The short answer is: no, light does not refract when it hits another beam of light in the traditional sense.

Here's why:

* Refraction is a phenomenon that occurs when light passes from one medium to another. This change in medium causes the speed of light to change, which in turn bends the path of the light. Think of light bending as it moves from air to water.

* Light beams themselves are not mediums. They are bundles of photons, which are particles of light. These photons do not interact with each other in the way that light interacts with a physical medium.

However, there are some interesting effects that happen when light beams interact:

* Nonlinear Optics: In some specific materials, under very high intensity conditions, light beams can interact with each other in a way that alters their properties. This is known as "nonlinear optics," and it can lead to phenomena like second harmonic generation (where light at one frequency is converted to light at double that frequency).

* Photon-Photon Scattering: At extremely high energies, such as those found in particle accelerators, photons can interact with each other directly. This interaction is very rare but has been experimentally observed.

In summary: While light doesn't refract in the usual sense when it hits another light beam, there are certain circumstances where interactions between light beams can lead to interesting and complex effects.