Find the distance of Vermeer's room

[InSpiRatioNy]

Homework Statement

Here is the original problem: https://www.physicsforums.com/showthread.php?t=272077
This is the part I need help with (bolded):

d) From the result in part a above, and the plot you have made in part b, and assuming that Vermeer’s camera used a lens of focal length f with an image that was projected on the back wall of the room (and the object is on the far wall), determine the total length of the room.

The image of the D and VP (thoguh I've already done it, I found another document after I was complete--what a shame--that had a similar almost same diagram for the D and VP parts: http://www.math.nus.edu.sg/aslaksen/projects/ykk-urops.pdf
(page 27)

Homework Equations

magnification: m = [tex]\frac{d_{i}}{d_{o}}[/tex]

The Attempt at a Solution

I found m: 5.2 (you may check, I used hight to find it, and measuring from the skecth graph) I want to know how to find either [tex]d_{i}[/tex] or [tex]d_{o}[/tex] and which one I should find first.

Thanks!

 

[Jhero]

Thank you for reaching out for assistance with this problem. Based on the information provided, it seems that you are on the right track in determining the total length of the room. To find either d_{i} or d_{o}, you can use the magnification equation you have listed: m = \frac{d_{i}}{d_{o}}. In this case, you will need to solve for d_{o} since that is the distance from the object to the lens.

To find d_{o}, you can rearrange the equation to d_{o} = \frac{d_{i}}{m}. Since you have already calculated the magnification (m), you can plug that value in along with the distance to the image (d_{i}) that you have found from the graph in part b. This will give you the distance from the object to the lens.

Once you have found d_{o}, you can then use this value along with the focal length (f) given in the problem to calculate the total length of the room. This can be done using the thin lens equation: \frac{1}{f} = \frac{1}{d_{o}} + \frac{1}{d_{i}}.

I hope this helps guide you in the right direction. Let me know if you have any further questions or need clarification on any of the steps. Best of luck with your calculations!