If you have your Photo data backup on the Time machine drive than definitely you will be able to retrieve the photos by restoring them from the time machine onto your macbook air.
If you don’t have the Time machine backup then you will have to do a data recovery by running data recovery software like Data Rescue 4.
" Important "
Unless you don’t recover your files from the trash, don’t trash any other items. If you trash any other items then the deleted files will be overwritten by the recent deleted files. The more you delete later, tougher it will get to recover your photo data with the recovery software.
Hope this helps......