There's Not Enough Light
Just in case you don't know yet....I would like to share with you this very old trick.
If in the future you'll get an assignment to shoot someone who's supposedly looking onto a computer monitor or a TV and wants the effect that the monitor is illuminating their face, forget about trying to capture that available light from the monitor to light your subject's face. It is just too weak.
Instead, put a speedlight there, zoom it out to its widest angle and set it at its lowest power and you'll be able to get the effect that you want as in the case of this photo.
All that remains is aligning everything together to get your desired effect.
Hope this helps. Happy shooting!
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Photo credits: Junpinzon.