Electronic – Suitable RC debouncing circuit

In your design, assuming you're using a common small signal NPN BJT (2n2222, BC547, 2n3904…), you're wasting about 20-30mA of current when the switch is closed. That is, about 10-15mA through the upper 220Ω resistor and 10-15 through the lower one. In addition, driving the base of the transistor with 10mA or more in this situation makes no sense: using a 10KΩ base resistor and thus reducing base current makes the circuit behave almost in the same way. That said, I would just avoid using the transistor, something like this should work:

^{simulate this circuit – Schematic created using CircuitLab}

I kept your values for R1 and C1, so the cutoff frequency of the circuit is similar to yours. I.e., the GPIO pin will not 'see' changes of the switch above about 5Hz (well, simplistic and not completely exact: see Wikipedia - Low Pass Filters for detailed info).

R2 is used as pull-down resistor: it is useful because it clearly pulls the pin to ground when the switch is open. Its value isn't critical, something between 10 and 150KΩ should be ok.

You need to transition on the screen going white within 0.5ms, transition on the screen going black within 10ms, but ignore periods of black lasting less than 4ms. This is more constraining than simple R/C circuits can provide: you need a timer.

The venerable 555 timer will do what you need. Set it up in monostable mode, with a duration of 6ms (make it adjustable), and drive the reset line from the output of your OPA141. Then, any glow from the screen will reset the timer, but if there's no light for 6ms then the output will go active. (You may have to play with the various polarities.)

An alternative would be using one of the simplest microcontrollers (e.g. an 8-pin PIC12) with an analog input. Less than $2, but incredibly versatile.