Final answer:
The correct safelight for a darkroom with blue-emitting rare earth screens is the GBX-2 filter. It provides safe illumination for radiographic materials. Blue-violet light is more sensitive to photographic emulsions due to its higher energy compared to red light.
Step-by-step explanation:
When blue-emitting rare earth screens are matched properly with the correct film emulsion in medical imaging, a GBX-2 filter safelight should be used in the darkroom. This type of safelight filter is specifically designed to provide the safe illumination required to handle radiographic materials without causing exposure or damage. It is crucial to have proper safelight conditions to prevent fogging of the film and ensure the highest quality diagnostic images.
The reason why photographic emulsions were historically more sensitive to blue and violet light is because blue-violet light contains a greater amount of energy than red light. Thus, blue-violet light has a higher frequency and, according to Planck's equation (E=h\u03bd), carries more energy which makes it more likely to affect silver halide crystals in photographic emulsions, leading to the image formation.
The behavior of light in different media, such as in the case of different wavelengths traveling through crown glass, relates back to differences in refraction which are dependent on wavelength. This property leads to different bending angles for different colors of light, evident in both everyday phenomena like rainbows and precise scientific applications such as spectroscopy.