Question

You are taking a photo of a poster on the wall of your dorm room, so you can't back away any farther than 2.9 m to take the shot. The poster is 0.60 m wide and 0.9 m tall, and you want the image to fit in the 15-mm x 22-mm frame of the film in your camera. Part A What is the longest focal length lens that will work? Express your answer using two significant figures. cm SubmitPrev Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining

Answer 1

Considering the 0.9m and 22mm magnification:
m = hi/ho =-0.022/0.9 = -0.025

Considering the 0.6m and 15mm magnification:
m = hi/ho = -0.015/0.6 = -0.025

So the full poster is covered by a magnification of -0.025

Note hi is negative as image is inverted (both vertically and laterally).
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To get the signs correct, we use m = -di/do.
Note the minus sign. E.g. see halfway down the link.

di = -m*do = -(-0.025)*(2.9) = 0.0725m

Then 1/f = 1/di + 1/do

1/f = 1/0.0725 + 1/2.9

f = 0.071m (=71mm)