Connecting MacBook Air M1 with iMac mid 2011 (Thunderbolt port)

Hallo

I would like to connect our MacBook Air M1 to an old iMac mid 2011 to use it as an external monitor via target display.

This means connecting a Thunderbolt / USB 4 ports (USB-c format) on the MacBook Air M1 to thunderbolt 1 on the old iMac.

I bought a cable converting usb-c to mini display port (same port as thunderbolt 1 and 2) would that work, still waiting for the delivery ?

I am still puzzeled how to connect the thunderbolt 4 (USB-c) to thunderbolt 1, there exist a thunderbolt 3 to 2 (https://www.apple.com/shop/product/MMEL2AM/A/thunderbolt-3-usb-c-to-thunderbolt-2-adapter). would that to the trick?

Thanks

Samuel