Derrel is spot on with his suggestions - especially metering first and then dialling the readings into manual mode is a great way to achieve constant exposure.
While the lights on a christmas tree appear bright to us, they are not at all. Shooting the christmas tree with a person and
keeping the mood in the scene is probably the most difficult shot you´ll ever try to create.
Last year I equipped a christmas tree with 1.200 LED lights in an attempt to get the most out of it photography wise. And I experimented pretty much with it.
The readings I´ve got with the shot below were 0,6 sec | f2,5 | ISO 100. The tree itself on this image is a little bright so one stop darker would still be enough for the blurred light background, but then the foreground would be darker too.
In order to achieve at least 1/100th which is still too slow if your kid really moves, you´d have to use ISO 6.400. Too much for a portrait in my opinion.
So using a flash as Derrel suggests is about your only chance. Nevertheless you´ll loose quite some light for the background (tree - christmas lights), as soon as you start bringing your ISO down, so at least for me - the image I have in mind is impossible to shoot with lower ISO.
AND: what you want to do is light the background with the flash as little as possible, because that will destroy the mood. So you need to:
- Get as far away with your kid from the background so that the flash doesn´t light it too much
- Get the flash as close to the kid as possible because any light source will always light objects that are closer to it much more than objects that are further away.
- To be able to get really close, use a light source that is big, but at the same time easily controllable (ideally a strip softbox with an attached grid, or a ring flash in front of your camera). If you´d use a speedlight without any light shaping tool and get really close, the images will look awful.
- Point the flash in a direction that it will not light the tree in the background (not possible with ring flash)
- Probably you´ll want a reflector on the opposite side of the light to bounce light back into the shadows that are created by the softbox with grid - a white foamboard will do.
One more thing to consider: if you want your christmas tree lights to look yellow, rather than white, (I have to disagree with Derrel) - you´d want to skip the orange filter, or even add a blue filter instead. If you use an orange filter, and later white balance the image for your orange light source, the tree lights will appear white. If you use a blue filter instead (or no filter at all), and later balance the whites to that blue (or neutral) light, the face of your kid will have nice skitones, and the christmas tree lights will be yellow.
All that sounds rather complicated, and it is to be honest. I always try to explain things with really easy words. But this one is the holy grail of photography. As crazy as that sounds.
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