How close would an LED have to be to your eyes to be as bright as the looking at the sun during midday? I wonder if it is possible to have an LED screen bright enough to simulate the brightness of our sun from Earth, and if so if it could be made small enough to fit on a laptop screen.
Typical sunlight has a power of a few hundred watt per square meter. A typical laptop screen has a power of about 4-5 watt. So obviously there is a vast difference in how bright they are.
To turn this into an astronomy question we can use magnitudes to answer it. The sun has apparent magnitude −26.7. A laptop at an arms length is about 50 lux, which would be about -18.4 apparent magnitude. So to get a solar apparent magnitude I need it to be 8.25 magnitudes brighter. That corresponds to a brightness increase of $100^{8.25/5}\approx 1995$. So if each pixel shone about 2000 times brighter, you would feel like the screen produced sunlight.
You could of course try looking at the screen more closely, making it brighter that way. However, the $1/r^2$ law for how brightness changes with distance stops being valid when your eye get closer to the pixel than the pixel lateral size. Worse, the amount of photons your eye can receive will also be limited by your pupil aperture: you cannot see all of the screen light. So this is why pushing your face against a screen doesn't make it feel like the sun (trust me, I tried this right now with my screen and some sample sunlight).
If it is a smaller region that is very bright surrounded by black it may feel brighter: good visual design can often fake a bit of extra brightness that is not physically there.
I don't see a physical reason for true sunlight intensity screens being impossible, but they are not practical. They would drain batteries like crazy. A visually convincing spectrum may still be doable with less power than a full blackbody spectrum (that would also emit a lot of infrared - nice feeling on the skin, but would heat up the screen a lot) just like LEDs faking white light with just a few frequencies.