Water softener drain to 1.5" drain

[linkin06]

https://imgur.com/a/kzxrBkY

I am trying to install a Clack water softener. It drains with a 1/2" tube, and my house was plumbed with I see a 1.5" drain in the wall. I am thinking of buying https://www.supplyhouse.com/Air-Gap...r-Filter-w-PVC-Trap-Adapter-1-2-Push-In-Inlet for the air gap, but i am not sure after this part, do I need to make a standpipe? Sorry, I am still learning.