Understanding Camera Zoom Lens Calculations

[tuomas22]

Homework Statement

A digital camera has a 3x zoom lens whose focal length can be varied between 6-18mm.
The lens is assumed to be thin. The image is formed on a CCD sensor whose diameter is 10mm.
1. How large an object can be captured with the camera if the object is at distance of 10m from the camera?
2. How close to the object must the photographer move if the object is the portrait of a human, which must fill the whole image area (can be approximated as a circle with diameter of 20cm)?
3. What is the distance between the lens and the CCD sensor in both cases?

Homework Equations

1/s + 1/s' = 1/f
M = s'/s = d/D (ccd sensor diameter/portrait diameter)

y'/y = -s'/s

s = object distance
s' = image distance
y = object size
y' = image size
M = magnification

The Attempt at a Solution

I have calculated the object size (first question), and got y = -y'*s/s' = -(-10mm * 10000mm)/6.0mm = 16.7m which is correct.

Then I tried to calculate the second question.

s = -s'y/y' = (-18mm * 200mm)/-10mm = 360mm = 36cm, but my teacher told me it is wrong and the right answer is 37.8cm, but I can't get that answer no matter what I try??

And for the 3rd problem, I should get answers ~6mm and ~18.9mm, but i have no idea how i get those. I tried with object-image relation equation, but I get ~6mm and ~18.03mm
(and if I use that 18.9mm for the 2nd problem, the answer is correct, but I can't get the 18.9mm anywhere, so I guess that's the main problem)

 

[Borek]

For the second problem - seems to me like 18 mm difference is a distance between lens and sensor. No idea how it is related to the question.

Third problem - I can't see how you can get a 18.9 mm distance if focal length can vary between 6-18 mm. That is, unless you are allowed to remove lens from the camera...

 

[tuomas22]

I can't see how you can get a 18.9 mm distance if focal length can vary between 6-18 mm

The image doesn't form exactly to the focal point, that's how it was explained. But i don't know how i can get the .9 addition to the 18mm

 

[Borek]

Question asked

What is the distance between the lens and the CCD sensor

Doesn't matter where the image forms, 18 mm is a technical limit of the camera.

 

[tuomas22]

well there must be something wrong because I lost 3 points (out of 6) with my answer :D

but I am with you, i don't understand either what I did wrong.

 

[tuomas22]

any other opinions? I'm afraid of the upcoming exam, if this question is in it, I know I only get half the points because it happened with homework too...

 

[Borek]

Haven't you tried to explain what was wrong with your teacher? TA? Whoever?