Easiest/cheapest way to light a redstone lamp when mobs fall through tunnel onto hoppers
Solution 1:
To detect if an item has been collected by a hopper, you can simply place a comparator adjacent to it, with the two-torch side touching the hopper.
The repeater then amplifies the signal so it does not matter how many items are in the hopper. Once we add an item...
We now know that there is an item in the hopper.