The direction of the reflected ray is determined by the law of reflection. The law of reflection states that the angle of reflection is equal to the angle of incidence. In other words, the reflected ray is reflected at the same angle as the incident ray, but on the opposite side of the normal (a line perpendicular to the surface at the point of incidence).

The direction of the reflected ray can also be determined using vectors. The incident ray can be represented as a vector pointing from the light source to the point of incidence on the mirror. The normal to the mirror can be represented as a vector pointing perpendicular to the mirror at the point of incidence. The reflected ray can be represented as a vector pointing from the point of incidence to the point where it intersects a plane parallel to the mirror and at a distance from the mirror equal to the distance from the light source to the mirror.

The law of reflection can be expressed mathematically as follows:

$$\theta_r = \theta_i$$

Where:

$$\theta_r$$ is the angle of reflection

$$\theta_i$$ is the angle of incidence