5V Fixed Voltage Regulator and Ripple Voltage

I have been experimenting with the common 7805 linear voltage regulator as a power supply.

To start I simply wired up the regulator with an resistor and led as the load.

Looking at the output of the regulator on my scope we can see a large ripple voltage of around +/- 1 volt!

I would prefer a nice and clean clean 5 volt output and in order to provide it we need to smooth out the supply voltage. Adding some larger capacitors on both the input and output of the regulator reduces the ripple we see above.

Two 100uF caps are added from input to ground and output to ground.

The result is a clean 5 volt output.

I picked the two 100uF caps because thats just what I had handy. Intuition tells me that larger caps will take longer to respond to the ripple voltage and that capacitors that are too small will not hold a charge large enough to compensate for the ripple. I do not know is how to determine optimally sized caps.

Also I really did not have a load on the output of the regulator. I am curious of the effect of a larger current draw in the circuit.