Find Largest Focal Length Lens for Photo of Poster - 2.79mm

[deenuh20]

Homework Statement

You take a picture of a poster on the wall of a room and maximum distance you can get from the picture is 3.1 m. The poster is 0.8 m wide and 1.2 m tall and you want it to fit in the 24 x 36 mm frame of the film in your camera.

What is the largest focal length lens that you can use? ____mm

Homework Equations

1/f = 1/do + 1/di
M=-di/do

The Attempt at a Solution

I have absolutely no idea how to go about this. What I tried, for starters, was find the ratio of the areas of the poster (0.96m^2) and the film (8.64E-4 m^2). I thought that by finding the ratio of the film to the poster would give me magnification which was equal to 9E-4. Then, using this number, I used the equation M=-di/do, plugged in 9E-4 for M and 3.1 for do and tried solving di and got -0.00279m. Then, I plugged this in the equation 1/f=1/do +1/di to solve for f and I got: 1/f=(1/3.1)+ -(1/.00279) = (-358.1 m) and took the inverse to be -0.00279 m. Then, converting to mm, it was -2.79mm.

 

[berkeman]

Don't use the ratios of the areas. Use the ratios of the sides.

 

[deenuh20]

Thank you very much. I finally got it!