An ideal diode conducts only when its forward direction matches the source polarity in this circuit model. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
A diode has a forward direction
With this source polarity, the shown diode direction gives a conducting path in the ideal fixed-drop model. Real diodes have curved current-voltage behavior; this model keeps one fixed forward drop.
forward direction⇒conducting path
The forward budget closes
The source is 12 volts. The LED drop is 2 volts, so the resistor gets 10 volts.
Vsource=VLED+VR=2V+10V=12V
Reverse orientation blocks
Reverse the same diode with the same source and limiter. The ideal model draws no branch current arrow.
Ireverse=0A
Forward current comes from the leftover voltage
For a forward-biased ideal LED, subtract the fixed drop first. The diagram shows the middle row.