The perception of an eagle's eye appearing red when viewed through a telescope or binoculars at night time can be attributed to the presence of blood vessels in the bird's retina. This phenomenon is not exclusive to eagles but is common among many diurnal birds of prey.
Birds have a specialized structure in their eyes called the "pecten." The pecten is a vascular and pigmented organ located in the back of the eye, near the retina. It helps nourish and support the retina, which is essential for their exceptional visual acuity.
The blood vessels within the pecten can reflect and scatter light, particularly when viewed through magnifying optical instruments such as telescopes or binoculars. This scattering of light can create a reddish appearance, similar to the red-eye effect that can occur in flash photography when light is reflected off the blood vessels in human eyes.
It's worth noting that this red appearance may not be visible to the naked eye or might be less prominent without the magnification provided by optical instruments.