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Thin lens equation question AAMC
Chloe_2125
#1 Posted : Saturday, June 19, 2021 5:53:22 AM
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Hi,

I am really having a hard time understanding how to approach the following question from the AAMC full length 1. I tried to use the "foil" (1/f=1/o +1/i) equation but I can't seem to get to the correct answer (B). Are you able to explain how to best solve this one?

O
^
__|______.__(.)
3F F

In the above figure, an object O is at a distance of three focal lengths from the center of a convex lens. What is the ratio of the height of the image to the height of the object?

A.1/3
B.1/2
C.2/3
D.3/2


Thank you in advance :)
INSTR_Katrina_128
#2 Posted : Tuesday, June 22, 2021 8:50:53 PM
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Oooh let me give it a shot!

Subbing everything into the FOIL equation, we get

1/f = 1/o + 1/i
1/f = 1/(3f) + 1/i

Solve for 1/i:

1/i = 1/f - 1/(3f)

Get a common denominator.

1/i = 3/(3f) - 1/(3f)

Add.

1/i = 2/(3f)

Flip both sides.

i = 3/(2f) = 1.5f

They're asking about "the ratio of the height of the image to the height of the object" which is LITERALLY the definition of magnification. 😁 So...

m = -i/o
m = -1.5f / (3f)
m = -0.5

The sign tells us that the image is inverted, but the question doesn't care about that.

The best answer is B.
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