A blackbody is also a perfect emitter giving off electromagnetic waves at all frequencies. A detector could measure the intensity of the radiation it receives through the prism. By moving the detector to different positions, you could measure the intensity of light as a function of color or wavelength.
So each wavelength has a finite intensity? If we consider wavelengths in the interval $[\lambda, \lambda + d\lambda]$ and each wavelength in this interval has a finite intensity, then the total intensity for this interval would be infinite because this interval has infinitely many wavelengths. Where am I going wrong? Are there not infinitely many wavelengths within this interval?
Between the red and green beams there are infinitely many beams with a finite intensity, so the total for this interval would be infinite?