Construct a table with two columns and four rows. Label one left column, "Current (mA)" for current in milliamperes. Label the right column "Brightness (mcd)" for luminous intensity in millicandelas.
Examine the current/brightness curve given in the manufacturer's LED specification sheet. Mark four points on the curve with your pencil and label them "1" through "4." Write the current level for the first point on the curve in the row one, column one of the table. Write the brightness level for the first point on the curve in row one, column 2 of the table. Continue in this fashion for the remaining three points you marked on the curve.
Subtract from the battery voltage (you are going to use to power your LED) the LED "forward voltage" from the manufacturer's specification sheet. Label this result as "voltage drop across the brightness resistor or Vbr." Divide Vbr by the highest current value in the table to determine the value of resistor you will need to make the LED the brightest. Label this result as "Resistor for highest brightness or Rb."
Divide "Vbr" by the lowest current value in the table to obtain the resistor value for the lowest brightness level. Label the result as "Rlb" for "resistor value with lowest brightness level."
Connect the positive terminal of the battery to the left lead of resistor Rbl. Connect the right lead of resistor Rbl to the positive terminal of the LED (anode). Connect the negative terminal of the LED (cathode) to the negative terminal of the battery. Observe the brightness level of the LED.
Replace resistor Rbl, the low brightness resistor, with Rb, the high brightness resistor. Observe that the brightness level is greater with Rb then with Rbl