I have built the circuit in LEDs and high currents and it works well - when the switch is open, the incandescent lamp lights up but the LED doesn't. When the switch is closed, the lamp goes out and the LED (actually an optocoupler) lights up.
I'm now trying to understand how it works, and also what value I should use for R1 below. For this exercise I've omitted D2 from the schematic and am assuming low resistance for D1. The bulb has a cold resistance of around 60Ohm, and I've arbitrarily multiplied that by 15 to get the hot resistance.
I have annotated what I believe to be values for P, I, V (and R where necessary) using my basic high school knowledge:
Here we see the current too low for D1 to fire, which is what was wanted. Total current is 8.5mA, well within the tolerance of the 2A transformer.
With the switch closed, the bulb can be ignored.The current at D1 now jumps and is enough to fire the LED. The total current is 0.3A, still way within the capacity of the transformer.
R1 needs to dissipate 2.13W.
I have found that I can use up to 100Ohm for R1 while maintaining adequate illumination in the lamp, and lower values for R2 while maintaining that switching functionality so want to play around with values in order to get R1's power value down - unless there's something fundamental about the circuit that would mean it stays the same.
My question then: I've used simple DC series/parallel formula for this AC circuit. Do those still hold or have I made some bad assumptions?