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I was looking at one of those new curved screens the other day and it reminded me of concave mirrors and the peculiarities about how they reflect light.

This image from the BBC found here should illustrate it:

reflection from concave lens

So if I am interpreting this correctly, the reflection should appear to be mirrored left of the focal point, but unaltered right of the focal point. You can reproduce this by looking at the inside of a spoon; things look flipped (in the case of a spoon, horizontally and vertically because it bends both ways), but as you hold the spoon closer and closer to your eyes, you eventually notice the reflection "snapping" into place and having the "right" orientation. Depending on the spoon this may be pretty close to your eyes, but in any case, it allows you to find the spoon's focal point.

This is were curved displays come in. Either I am mistaken in my assumption that they should also have a focal point - the assumption here is that surfaces that reflect light and surfaces that emit light both have a focal point as long as they're both concave - or I am mistaken about how to find the display's focal point.

In my experiment, I start standing very close to the display, and see the image unaltered, as expected. Once I start moving away, I expect to see the image flip horizontally if I just move away far enough. But that point never comes. I came to a distance of about 20 yards and the image still had not flipped. (Unfortunately I couldn't go further as there was a wall behind me.)

Granted, these displays all seem to be curved only slightly, so perhaps the focal length is just really long? If I am right about this, does the curvature of the screen in a movie theater dictate how many rows the movie theater can have? Or do concave sources of light not have a focal point?

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No, a curved display will never flip the image it displays.

Consider two lamps stacked on top of each other. Why can a curved mirror flip the image of this object upside down? Rays of light from each lamp hit the mirror and then hit your eye. The image of the lamps looks flipped to you if the ray from the upper lamp hits your eye coming from a lower angle, and vice versa. This is only possible if a reflection occurs.

When you have a computer screen, there is just light coming straight from the screen itself. If you have the computer display a picture of two lamps stacked on top of each other, the light from the upper lamp will always hit your eye at the higher angle, so the image is not flipped.

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