How to increase (optical) power of arduino circuit with LED? Increasing current with fixed voltage
Since P=IV, and the Arduino has a fixed voltage of 5V


Optical or Radiometric power measured in mW is not the same as the electrical Forward Voltage x Forward Current. 

226mW of white light is about 50-60 lumens.  You need about 350 mA to get 50 lumens out of a 50 lumen white LED. 

To get 223mW out of colored LEDs you need a fair amount of lumens.
You must convert radiant mW to lumens by the wavelength of the color.



Lumens required for 223mW radiometric optical power


red 58 lumens
green 152 lumens
blue 6 lumens





  Arduino has a fixed voltage of 5V


Supply voltage does not matter.  An LED is a current regulated device and it's voltage is a function of it's forward voltage, typically 2V (red) to 3V (white. green, blue) .  The other 2-3V (of the Arduino 5V)  will be dropped across the current limiting resistor.




  Wouldn't the current be ~10 mA(5/470) to account for the 470 Ohm
  resistor and 5V EMF source?


A 300Ω resistor will give you 10mA with a 2V LED.
A 200Ω resistor will give you 10mA with a 3V LED.

You need a 1 Watt high brightness high efficacy LED which will still take over 300mA with a 5Ω-8Ω current limiting resistor.