The 'Cos Theta' Effect?

The other day when I visited the Reliance Fresh supermarket near our home a poster on the wall grabbed my attention. The poster showed the image of the model, well-known in this part of the country, who is none other than the film-actress-cum-model Genelia. Her cocquettish look is paticularly arresting even for a supersenior person like me. I'd parked my scooter a few meters away and looked at her image from an angle. She was still looking at me eventhough I was not in front of her! That was quite flattering!! Next moment my mind struggled out of the sensuosity of Genelia's looks and turned to the left half of my brain to check as to why one feels that a model is looking DIRECTLY at you from whichever angle and distance you look at her. 

This effect is of course familiar to all of us and we tend to take it for granted. I haven't bothered so far to check whether someone has attempted to explain it.  Maybe someone has.....

 Here is my explanation of the phenomenon, which emerged thanks to Genelia's compellingly cocquettish gaze!!

The model's two eyes are in a PLANE in the two-dimensional poster unlike if she had been standing there in person. In the latter case her pupils would have been at the centre of the white globular 'eye-balls' (may be my terminology is physiologically imprecise). In the poster also the pupils would be at the centre of the eyeballs.

In the latter case if you look at an angle 'Theta' with the line perpendicular to the plane, the entire width of the  image will be a projection into your view 'Cos Theta' times the width of the image. (Incidentally 'Cos Theta' is a trigonometric function familiar to maths students.) So the tranformation of the image widthwise is LINEAR. That means the pupils will still be in the centre of the eyeballs. Hence the model will appear to look at you DIRECTLY irrespective of the viewing angle.

On the contrary if Genelia had been there in person and she was looking directly at you when you were ecactly in front of her and UNLESS she turned her gaze (which possibility would depend on whether you really impressed her!) towards you when you looked at her from an angle you wouldn't feel she is looking at you.

The reason is that the eyeballs are in reality (in contrast to a picture)  curvilinear and its projection in an angle with the perpendicular will not be a LINEAR  tranformation but will be a NONLINEAR one. So the pupils will not be in the CENTRE of the eyeballs. Consequently Genelia's frontal gaze will remain frontal!

Do you now see the value of plane posters of models for advertisement as contrasted to their statues, which would only cost the advertiser far far more,  while depriving him of the ego-boosting of the viewer, which a poster image would achieve to the ad man's advantage!

I like to call it the 'Cos Theta' effect!

(A few snaps of the poster from different angles follow. Because of the glass sheet covering the poster the pictures are of poor quality, though! Also appended is a graphic explanation of the curvilinear transformation referred to above)