at the back of something—
1. behind smth.:
- At the back of the house there was a large garden.
2. in the part which is farthest from the front:
- a room at the back of the house; a door at the back of a building.
3. responsible for smth., especially smth. bad:
- Mr. Tillotson is at the back of the plan to demolish those fine old buildings.
on the back of something—
1. on the reverse side of smth.:
- On the back of the letter was a diagram.
2. in addition to smth.; immediately following smth. (usually of an unfortunate event):
- The child had the measles, and then on the back of that came the scarlet fever.