I was wondering if light can be reflected how can someone reflect X-ray of what material does it need to be made of and is its design completely different to that of our original mirrors? Does this mean during long-space voyages in which radiation is an problem why can scientists not develop large panels of X-ray mirrors and Gamma-Mirrors and simply reflect the radiation off rather than worry about that?
Unfortunately X-ray and gamma mirrors are impossible to build the way you think - mainly because there is much less interaction with the matter comparing to UV - it will go through all materials commonly used for making mirrors. Even for EUV light (wavelength of 13.5nm) building effective mirrors is a royal pain.
As wavelength of X-Rays is very small (down to 0.01nm) you cannot build dielectric mirrors, as this would require depositing dielectric layers which are less than 1 atom thick.
It is only possible to reflect X-Rays at a very shallow angle (see Kirkpatrick-Baez X-Ray lens design), so you cannot use this for shielding of radiation coming from all directions. Gammas are even worse - the only thing you can do is to bring alot of mass.
Yes it is possible but as BarsMonster points out it isn't like an optical mirror. X-ray reflectors are used in the construction of nuclear weapons and are critical to increasing the yield. How they work is the initial fusion reaction releases high energy radiation, this is then reflected back into the reaction mass increasing the energy levels of the reaction mass causing a sort of radiation implosion.
The reflector is typically a cylinder made of a material such as uranium. The primary is located at one end of the cylinder and the secondary is located at the other end. The interior of the cylinder is commonly filled with a foam which is mostly transparent to x-rays, such as polystyrene.
The term reflector is misleading, since it gives the reader an idea that the device works like a mirror. Some of the x-rays are diffused or scattered, but the majority of the energy transport happens by a two-step process: the x-ray reflector is heated to a high temperature by the flux from the primary, and then it emits x-rays which travel to the secondary. Various classified methods are used to improve the performance of the reflection process.
Since these type of reflectors are typically used in weapons research there is not much public data on them. However here is a rough illustration of what an x-ray reflector looks like in the second stage (reference).
There are a lot of X-ray mirrors in space and around the world. Applications are X-ray astronomy, synchrotron sources, some medical and litographical application. So it is not something theoretical.
All these mirrors have in common is to reflect light at grazing incidence, they are shaped in way to focus the light in a same way that happens for visible light with visible optics, however this is the reason why mirrors focus, not if and why they reflect X-rays.
Several physical principles are used to reflect light depending on the energy (metallic coating, multilayers or crystals). However the question asks if these mirrors can be used to deflect the radiation for human space travel, and the answer is no, because when radiation hit at a large angle they don't act as mirrors any more, but act more like shields.
At this point is more practical to directly use shields (absorbing material), depending on energy it can mean to carry a good amount of extra-weight in space.