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You can specify a chain of events if you like, such as DDS, meaning Diffuse event to Diffuse event to a Specular in that order. The LPE would collect anything that happens in this specific order and store them. For simplicity we'll cover more common cases first.

Direct and Indirect Light

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There is a funny thing about specular objects without diffuse shading, they only look like the things they reflect. If you were to render the Cornell Box scene examples with perfectly specular surfaces and a light, all you would see are reflections of the light. What does a mirror look like? Can you describe a mirror that has nothing to reflect? Or does the mirror look like what it's reflecting? This is why indirect results are so important for realism and ray tracing.

A diffuse scene using subsurface and translucent effects.

A specular scene using iridescence and transmission (glass)