How to calculate simple transistor switch. How to light LED in the dark

I needed to make LED light in the dark, so I found this video, where Ben Krasnow explains how to make a simple transistor switch.

How i computed the circuit.

The cheapes phototransistor i could obtain was L-53P3BT by KingBright.

It's parameters:

Here we can see that maximum collector - emitter voltage is 30 V, max current is 3 ma. 

Now i need transistor that can handle 5 V and 20 mA through emitter, and with hFE > 20 / 3 = 6.6. I have PN2222A

As we can see hFE is about 75. Maximum current is 800 ma, max voltage is 40 V. It's more than enough.

Now calculations, collector must have 20 mA. So transistor base current must be 20 / 75 = 0.267 мА. It's less than 3 ma, so everything should work.

Calculate resistor value:

5 / 267 * 10^-6   = 5 / 0.00000267 = 18727  Ohm.

So i should use 19 KOhm. I had more than 5 V, so i used 30 KOhm.

Circuit

It's also a simple LED driver, we can connect as much LED's as much voltage we have.

If we connect identical LED's there will be no difference in brightness, if we have enough votage.

If we need more amplification of sensitivity, we can connect transistors in cascade (emitter of the 1 transisor to the base of 2), then hFE = hFE_1 * hFE_2

In our case we would have hFE = 4900.