The human eye has a lot in common with a pinhole camera, being essentially a sma
ID: 2198062 • Letter: T
Question
The human eye has a lot in common with a pinhole camera, being essentially a small box with a hole in the front (the pupil) and "film" at the back (the retina). The distance from the pupil to the retina is approximately 24mm . Suppose you look at a 180-cm-tall friend who is standing 7.4 in front of you. Assuming your eye functions like a pinhole camera, what will be the height, in mm, of your friends image on your retina? Suppose your friend's image begins to get bigger. How does your brain interpret this information? (Does he come closer? Goes away? walks to the right or left?)Explanation / Answer
Snell law doesn't work here because this question has got nothing to do with a refraction. In fact, it's got more to do with geometry than physics. Let's denote: d = 24 mm = the distance retina-pupil, H = 180 cm = the height of a man and D = 7.4 m = the distance between the man and the eye. Consider now two light rays. The first leaves the top of the man's head, goes through the pupil and falls into the retina. The second one leaves the bottom of his feet and proceeds through the pupil as well. If we neglect the fact that the retina is curved, then the rays that we have just drawn form two similar triangles that share the same top (the pupil). Now we apply intercept theorem for similar triangles and write: H/h = D/d and from here h = d x H / D = 0.024 m x 1.80 m / 7.4 m = 0.00584 m = 5.8 mm.
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