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 0.70 m wide and 1.05 m tall, and you want the image to fit in the 15-mm × 22-mm frame of the film in your camera.What is the longest focal length lens that will work?
Express your answer using two significant figures.

Answer 1

Here, consider the 1.05 m and 22 mm magnification:
m = hi/ho = - 0.022 / 1.05 = - 0.0209

And consider the 0.70 m and 15 mm magnification:
m = hi/ho = -0.015 / 0.70 = -0.0214

Therefore, the full poster is covered by a magnification of – 0.0214

Note hi is negative as image is inverted (both vertically and laterally).

To get the signs correct, we use m = -di/do.

so -

di = -m*do = -(-0.0214)*(2.9) = 0.062 m

now use the lens formula –

1/f = 1/di + 1/do

put the values -

1/f = 1/0.062 + 1/2.9 = 16.46

=> f = 1/16.46 = 0.061 m = 61 mm

So, the longest focal length of the lens = 61 mm.