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! :)
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.
Ohhhhhh I get it now! I was imagining the scenario in a completely different way. Thank you!
To calculate the apparent size of an object, you can use the formula:
Apparent size = Actual size / Distance from the object
In this case, the actual size of the object is given as 1 cm and the distance from your eyes is given as 80 cm. Plugging these values into the formula, we get:
Apparent size = 1 cm / 80 cm
To simplify this, divide 1 cm by 80 cm to get the apparent size in terms of a fraction or decimal. The resulting value will tell you the apparent size of the object when it is 80 cm away from your eyes.
To find the apparent size of an object, we need to determine the angle it subtends at the observer's eye. In this case, the object is 1 cm long and is held 80 cm away from your eyes.
To calculate the angle, we can use trigonometry. We know that the tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is 1 cm (the length of the object) and the adjacent side is the distance from your eye to the object, which is 80 cm.
So, we can apply the tangent function to find the angle:
tan(theta) = opposite/adjacent
tan(theta) = 1/80
Now, to solve for theta (the angle), we need to find the inverse tangent (also known as arctan) of both sides:
theta = arctan(1/80)
Using a calculator or a math software that has the inverse tangent function, you can find that the angle theta is approximately 0.72°.
Therefore, the apparent size of the object held 80 cm away from your eyes is approximately 0.72°.