The Planetary Light Curve

I know that light can be affected by gravity. But what if there was a planet where if you shone a light in a direction and it could hit your back. I'm talking about a planet where light is bent around the diameter of the planet and back to the starting point. But I am not incredibly good at math so I need help.

The planet must be made of Osmium. Although that is the logical material anyway because I want this planet to be as small as possible without being compressed and Osmium is the densest naturally occurring element (assuming it won't compresses itself under its own gravity for some random reason). And it must be natural because I want this to be possible. So using this information I wanted to know the diameter of this planet for light to bend all the way around it and I would like to know the gravity of this object.

I just want a "defy all odds" answer. Many other areas of Q/A in SE have been calling me ridiculous and that my idea is useless but I don't want criticism, I just want your answers.

@Tim B has given an amazing answer but we can't do the math. If anyone could help that would be great.

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The Planetary Light Curve

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