Yes, the length of a shadow does depend on the height of the person or object casting the shadow. The basic principle behind shadow formation is the blocking of light by an opaque object. When an object is placed in the path of a light source, it obstructs the light rays, creating a region behind it where the light does not reach. This dark area is the shadow.
The length of the shadow is determined by the angle at which the light rays hit the object and the distance between the object and the surface where the shadow is cast. The taller the object, the longer the shadow it casts, assuming the light source and the surface remain the same.
If you imagine a person standing under the sun, for example, during the morning or evening when the sun is lower on the horizon, the person's shadow will be longer compared to when the sun is directly overhead during midday. This is because the lower angle of the sunlight results in longer shadows being cast.
Similarly, if you have two people of different heights standing side by side under the same lighting conditions, the taller person will typically cast a longer shadow compared to the shorter person.
It's important to note that other factors, such as the position and intensity of the light source, the angle of the surface where the shadow is cast, and the presence of other objects, can also influence the length and characteristics of a shadow.