dvd drive on iMac 2011

Welcome to the Apple Support Communities.

Have you read these troubleshooting steps from Apple Support: Get help with the slot-loading SuperDrive on your Mac computer - Apple Support?

If your SuperDrive still doesn't work, you could use an external optical drive, however, considering the age of your Mac, it may be best to put resources into a new Mac, as yours has not received a macOS upgrade in over 4 years, is obsolete, and any other component could fail at any moment.

Here is the current Mac product lineup: Mac - Apple.

Apple also has refurbished Mac computers: Refurbished Mac - Apple.

Cheers,

Jack

As Jack stated an external usb dvd drive will work, with the added benefit that if and when you do replace your iMac the external will still be useful since modern iMacs no longer have them.