hi,
You really should consider the circuit inputs as whole circuit.
Say the LDR resistance is equal in value to the 10K series resistor, ie: both 10K
that would make pin2 of the 741 approx 6V [Vs/2].
If you now adjust P1 the 10Kpot to its centre of rotation, then pin3 of the 741 would be at about 6V.
The output pin6 of the 741 could be either high or low. [12V-2V] or +1.2V.
Adjusting P1 about its central rotation would cause the output to switch high or low.
If pin3 voltage is higher than pin2 the 741 output will be high, if pin3 voltage is lower than pin2, the output will be low.
As the LDR resistance changes with the intensity of light falling on it, so will the voltage on pin2, this switches the 741 output high/low depending upon the light intensity.
Using a 470R at either end of the pot, means that voltage on pin3 cannot be set higher than +11.5V or lower than +0.5v.
So the voltage on pin3 is from +0.5v thru +11.5V, which IMO is too greater range, it makes the setting of P1 'coarse'.
A point to note, some comparator ic's will go into output inversion if the inputs exceed Vsupply -2V, ie: 10V.
A far better design would be based on knowing the resistance range of the LDR when used in this project, the resistors would be calculated to give the operating range of P1.
OK.