How Do You Choose the Right Lens for Photographing a Building at 490m?

[Maria H]

Homework Statement

A building will be photographed with a camera.

The distance is 490 m to the building.
The building height is 85m and width 40m.
You can choose between 35mm, 50mm, 135mm and 250mm lenses (focal length of lenses).
Select the lens that gives the largest image of the building (whole building should be in the movie). The film has a frame on 24mm36mm.

a) Which lens do you choose?
b) How large is the image of the building? Reply with rounded integer.
c) How large is the distance between the lens and film? Suppose that the lens thickness is negligible. Reply with two decimal places.

Homework Equations

1/a+1/b=1/f
1/a=1/b
h/H=c/d(?)

The Attempt at a Solution

40/0,036=1111,111.. 490/1111,111=0,411 (focal length 411?) I think I'm lost already here.
Or,
1/40+1/0,036=1/f f=0,0359.. (I'm not sure if this means that 35mm is right or if 50mm is better since it 35,9mm)

I'm not sure how to use h/H right know.

I would be so happy if someone could help me!

/Maria

 

[rl.bhat]

Hi Maria H, welcome to PF.
If a is the object distance and b is the image distance, then
magnification m = h/H = b/a.
Lens equation is
1/a + 1/b = 1/f rewrite it as
1 + a/b = a/f.
1 + 1/m = a/f.
Substitute the values and find f.

 

[Maria H]

Hi Maria H, welcome to PF.
If a is the object distance and b is the image distance, then
magnification m = h/H = b/a.
Lens equation is
1/a + 1/b = 1/f rewrite it as
1 + a/b = a/f.
1 + 1/m = a/f.
Substitute the values and find f.

Thank you very much Rl.Bhat!

Okey, this is what think.

1/490m+1/0,036m=27,7798.. 1/27,7798..= 0,03599m 35,99mm

It means that a focal length of 35mm is to short. The photografer have to use the length of 50mm. Right?

Now I have. a=490m f=0,050m

If I use 1 + 1/m = a/f with m=h/H i get a very strange result. just a few mm. I think it should be rather around 35 an 50 mm.

I think it would help if a kind soul could show me the steps to find the result to these tasks.
The only think I feel sure about is that a focal length of 50mm i correct.

/Maria

 

[rl.bhat]

Your calculation of F is not correct. I think you have made mistake in calculating m.
1 + 1/m = a/F
1 + 85/36*10^-3 = 490/F.
Now calculate F