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If we place two plane mirrors facing each other wouldn't the image produced by the first mirror act as a virtual object to the second mirror? If so, would the image produced by the second mirror then be a real or virtual image? Please explain how to identify real and virtual images as I think my understanding might be flawed.

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All the images a plain mirror can make are virtual. i. e. you can make a real image only with for example a lens, like in your ey or in a camera. real images you can project on a screen or your retina or a photo plate . Virtual pictures are pictures only for the ey or camera "real". the light rays seem to come from points where you localize the virtual picture, You should learn how to find virtual pictures in a mirror.

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