# Math Analysis

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What is the apparent size of an object 1 cm long held 80 cm from your eyes?

==> When they say "apparent size", they mean the angle from which one object is viewed by, say, a person (or in this case a pair of eyes). I thought I'd be able to find the angle by using the formula s = r*a (arc length [or diameter] equals the radius times the angle). However, I'm missing the diameter of the eye, so I can't use this formula. Does anyone have any idea how to solve this? Any help is GREATLY appreciated! :)

• Math Analysis -

Apparent size would be a measurement of subtended angle in this case. It would be 1/80 radian, which is 0.72 degrees.

You could also approximate it as arctangent 1/80, and get very nearly the same result

It has nothing to do with the diameter of the eye.

• Math Analysis -

Ohhhhhh I get it now! I was imagining the scenario in a completely different way. Thank you!

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