The first optical element that the laser interacts with on the optical table is a beam splitter. This splits a single laser beam into two. Fundamentally, this is based on the Fresnel equations. Particularly when it is dark outside, you might have noticed that your reflection is visible in a window. This indicates that a window not only transmits light, but also reflects a part of it. The amount of light that is transmitted depends on the angle of incidence, the material’s index of refraction and the polarization of the light. The precise amount that is reflected or transmitted can be derived by using Maxwell’s equations and some trigonometry to result in rather complicated looking equations.
This is basically all that is needed to explain a beam splitter. The beam splitter’s mirror is oriented to be at 45° with respect to the laser beam, such that there is a 90° difference between the transmitted and the reflected beam.