The thermal condition of a silicon substrate in a rapid thermal processing system using circular infrared lamps and specular reflectors is systematically studied based on the direct approach model using a ray trace simulation with resolving the number of reflections, for the first time, in order to clarify the mechanism that the thermal condition for the silicon substrate is not sensitive to the distance between the circular infrared lamp and the reflector base plate forming the region behind the circular infrared lamp. Since total reflection from the specular reflectors behind the circular infrared lamp causes no energy loss on their surface, the intensity of the ray emitted from the infrared lamp toward the reflector base plate can be maintained and transported to the silicon substrate surface, even if the distance between the circular infrared lamp and the reflector base plate influences the path of the rays which are approaching the silicon substrate. Therefore, it is concluded that the thermal condition of the silicon substrate can be robust to the geometry of the specular reflectors behind the circular infrared lamp.