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When to apply backface culling, depending on the ray and material type?

I am currently implementing a ray tracer, which supports reflection and refraction. I have the following types of rays:

  • camera rays
  • shadow rays
  • reflection rays
  • refraction rays

I have the following types of materials:

  • diffuse (opaque, do not reflect)
  • purely reflective (opaque, but can reflect)
  • reflective and refractive (semi-transparent objects such as bodies of water, which can reflect part of the light ray and refract the rest).

For which combinations of ray type and material type of object being hit should I perform backface culling, when determining the hit point of a ray on a triangle?