Originally Posted by Barry2

When you go from Large Front Ring & Large Rear Cog to Small Front Ring and Small Rear Cog there is a considerable difference in the length of chain needed.
This difference is calculated using the teeth difference.
In your case (50 front + 50 rear) - (39 front + 10 rear) = 51
100 - 49 = 51 teeth capacity

The rear derailleur has to be able to take up the slack in the chain for this 51 difference.

Rear Derailleurs are rated in two ways

Capacity (in your case 51)
Max rear Cog (in your case 50)

You are going to have a really tough time finding a Rear Derailleur to meet both these requirements at the same time.
But know you know what your looking for!

All the best

Barry