Scored c/p #45 help??

[purplefrog13]

The options are
a) 1/3
b) 1/2
c) 2/3
d) 3/2

The answer is 1/2, according to aamc. But even with the explanation for the question. I still don't understand, so if anyone knows how to explain it better...I would greatly appreciate it! I don't quite understand what the meaning of ' is in the AAMC answer, or the equation used in general.

"This is a Physics question that falls under the content category "How light and sound interact with matter." The answer to this question is B because the ratio of the image height to the object height is equal to the ratio of the lens-image distance to the object-lens distance. According to the thin lens equation, the distance between the lens and the image is 3F ' 1F/(3F-1F)=(3/2)F, where F is the focal length. The ratio sought is then equal to (3/2)F/(3F)=1/2. IT is a Scientific Reasoning and Problem Solving question because you are asked to determine and use scientific formulas to solve problems.

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[doctor.octopus]

i = image distance
o = object distance
f = focal distance

i/f = 1/i + 1/o (lensmaker's equation)

we rearrange that to say: i = (o * f) / (o - f)

that part is just algebra.

so, f = 1F obviously, and we're told that o = 3F, so to plug in:

i = (3F * 1F) / (3F - 1F)

i = (3F/2)

now, to get magnification m, we use the equation: m = -i/o

m = (3F/2) / (3F) = 1/2

 

[doctor.octopus]

I think the ' in the answer is supposed to indicate multiplication.

 

[purplefrog13]

Excellent! Thank you!