This is a Halogen Bulb 50W 12V Dimmable GY6.35 T4 JC Type Capsule Bulb. It fits the lamp shown in the other photo, behind the smoky glass.
Please note that it has pins, not the more common D shape connectors.
I needed to replace one, but had to buy a pack of ten. So please let me know if you'd like a couple.