Can I use the power connector from an old 2006 13" Macbook on a new 11" macbook air with the MagSafe to MagSafe2 converter?

I have an old 2006 Macbook with the original Magsafe power adapter charger and I'm buying a new 11" Macbook Air, which comes with the new Magsafe 2. I wanted to know if I should buy the optional Magsafe to Magsafe-2 converter? Will the converter work with a charger as old as the original 2006 Magsafe? Could it damage the macbook air at all?

Apple 45W MagSafe Power Adapter for MacBook Air

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