A bit of eye basics is needed here
Firstly a bit of simple biology.
Red eye in humans is caused by light reflecting off the tapetum lucidium, a layer just below the retina that is filled with blood vessles. When an intense light such as a camera flash firing occurs the eyes pupil contracts but too slowly to stop the reflection of the redness of the tapetum.
Red eye is guaranteed to occur with the human eye if the flash is located less than about 2.5 degrees off axis to the eye.
Animals such as cats and dogs have eyes designed to see far better at night than us poor humans, so they have a different physiology of the eye. The 'red eye' and silver 'eye' are actually caused because they have a far more reflective tapetum lucidium than humans have. The tapetum lucidium in most animals that are nocturnal or have evolved from notcurnal animals reflects light back on to the retina and it's rods and cones thus increasing their night vision sensitivity.
The angle for red eye in animals varies greatly depending on the animal species, the size of the eye and how dilated the pupil is. As a general rule where possible use bounce flash off the ceiling or flash located a foot or more to the side or above the camera to eliminate red eye and silver eye from animal photos
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