I have always found it a bit disconcerting when looking at portrait photos where the subject or subjects are looking out of shot rather than at the camera. This phenomenon is due to the fact that we, as humans, and being part of the inquisitive animal world, like to have eye to eye contact when we look at other beings.
It’s probably something you never really gave much thought to, but in photography, it is very important to consider where your subject/s are looking when you compose your shots.
In photographic composition, we can utilize guiding lines, such as pathways, winding roads, fences, tree lines, etc., to draw the viewer’s eye from one point to another. These guiding lines are obvious to us because they are there as part of the make-up of our images.
However, the invisible line between our subject’s eye and what he/she/it is looking at is not obvious to us because we cannot see it - but it is there nevertheless. It connects with us and it is a very important link as to 'viewer impact' of our images. It can change the focal point (the main point of interest) as well as the mood and/or emotion of the image.
To give an example:
A little girl is posing in the garden whilst holding ‘and looking at’ some flowers. Because she is looking at them, the interest is taken away from her and the flowers become the focal point. There is an invisible line drawn between her eyes and the flowers. This draws attention away from her.
If the child was looking directly at the camera, the focal point would be placed squarely on her and the flowers would then become a secondary point of interest.
A different scenario is when she is neither looking at the flowers or the camera but is gazing at some other object out of view, this can become an annoyance because the viewer also wants to see what it is that has grabbed her attention. It would be different if she was just sitting there, gazing into space, because you know that she is not looking at anything in particular.
A similar case to this is at a wedding and you are taking photos of the bridal party whilst they are being photographed by the official photographer. But I suppose in this case you know where they are looking, but it can still be quite bothersome.
Now, when you are taking portrait photos of family or friends, you are going to have to make a conscious decision as to how you will portray them. If they are side-on or profile shots, with the subject looking out of frame, at least place them in the frame so that they have plenty of space to look into. In other words, if your subject/s are looking to their right, place them 1/3 in from the right of the frame, so that they have about 2/3 of the frame to look into. Still having both eyes in view with the focus being on the eye nearest the camera.