This is a simple BJT circuit, the LED turns on when the input voltage reach a level which can be estimated from the values of Vbe, base-emitter shunt resistance (Rbe), and the series resistance Rb. Resistor Rbe raises the threshold of the circuit, this is because the current from Rb is shunted away from the base. Thus, the transistor remains off until the input signal is at a level where it can deliver an amount of current greater than that demanded by the base-emitter shunt resistance. Based on voltage divider, the threshold can be estimated by this equation
Vthr = (Vbe)(Rb + Rbe)/(Rbe)
In this circuit
Vthr = (0.75 V)(10kOhms + 15kOhms)/(15kOhms)
Vthr = (0.75 V)(25kOhms)/(15kOhms)
Vthr = 1.25 V
This is not very precise but adequate to provide good guidance to a designer.
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