To compute shadows secondary rays known as shadow rays would be fired out from the intersection position of normal rays. These shadow rays would be aimed towards the light source in the scene and would be checked for intersections with other objects. If an intersection occurs then the light source is occluded from the original object at the point of intersection and therefore should be in shadow.
The ray-tracer also uses these shadow rays as part of its two different types of lighting: point lighting and area lighting. Point lighting is a light source at a specific point in the scene and changes the colour of objects based upon its colour and intensity as well as its distance away from the object in question. Area lighting is a light source covering a defined area. It uses multiple point lights within the area to determine average lighting values. Point lighting provides hard, distinct shadows whereas area lighting produces softer shadows.