A 35-mm camera equipped with a 40-mm focal length lens is used to photograph a tree 17 m tall. If a 32-mm high image of the tree on the CCD sensor is required, how far should the camera lens be from the tree?
Show Work Please!
Thank you so much!
just review your formulas. In particular,
hi/ho = f/f-do
32mm/17m = 40mm/(40-do)mm
32/17000 = 40/(40-do)
do = 21210mm = 21.21m
To find the distance the camera lens should be from the tree, we can use the similar triangles formed by the camera, lens, and tree.
Let's denote the distance the camera lens should be from the tree as x.
We have the following information:
- Focal length of the lens = 40 mm
- Height of the tree = 17 m
- Height of the image on the sensor = 32 mm
Using the similar triangles, we can set up the following ratio:
(tree height) / (distance to tree) = (image height) / (focal length)
Plugging in the values we know:
17 m / x = 32 mm / 40 mm
To make the units consistent, let's convert mm to meters:
17 m / x = 0.032 m / 0.04 m
Simplifying the ratio:
17 m / x = 0.8
To solve for x, we can cross-multiply:
17 m * 0.8 = x
x = 13.6 m
Therefore, the camera lens should be approximately 13.6 meters away from the tree.
To solve this problem, we can use the concept of similar triangles.
Let's denote the height of the tree as H and the height of the image on the CCD sensor as h. We are given:
- H = 17 m
- h = 32 mm = 0.032 m (since 1 mm = 0.001 m)
Now, let's set up the similar triangles. The ratio of the tree's height to the image height should be the same as the ratio of the distance from the tree to the lens (let's call it D) to the focal length of the lens (let's call it F).
The ratio can be represented as:
H / h = D / F
Plugging in the values we know, we get:
17 / 0.032 = D / 40
Now, we can solve for D by cross-multiplying and then dividing:
D = (17 / 0.032) * 40
Calculating this, we find:
D ≈ 21,250 m
Therefore, the camera lens should be approximately 21,250 meters away from the tree in order to produce a 32 mm high image of the tree on the CCD sensor.