Final answer:
The penumbra size varies with the light source size because, according to the inverse square law, light intensity decreases with the square of the distance, causing it to spread thinner the further it travels. With larger light sources, there's more area for light to emit, resulting in a larger penumbra.
Step-by-step explanation:
The amount of penumbra differs with the size of the light source due to the way light spreads out and weakens as it travels. According to the inverse square law, the illuminance or light intensity is inversely proportional to the square of the distance from the light source. As light travels further from the source, the area it must cover increases exponentially, meaning the light is spread thinner over a larger area. This is why a light source's penumbra, which is the partially shaded outer region of the shadow cast by an opaque object, varies in size. With a larger light source, the penumbra increases because there is more surface area emitting light, making the edges of shadows less defined and broadening the penumbra region.