Currently Blender's Cycles does not have an official way of catching light from something such as the lamp. There's a thread about it on the Blender devtalk page explaining all it's limitaitons.

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The only way around this that I know of is to:

1. Use a different render engine. I don't know what to suggest as I haven't worked with any others.
2. Do some compositing tricks.

Someone has a guide listed here: https://www.reddit.com/r/blender/comments/49b5l3/shadow_and_light_catcher_thought_it_might_help/

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I also included a guide in the comments of this post, but I'm unsure how physicially accurate it is and there are probably much better was of doing it now.