Optics, camera lenses and object height/size

In summary, a camera with a focal length f of 6 cm is used to take the picture of a person who is 180 cm tall, standing at a distance of 3 m in front of the camera. The image size can be determined using the thin-lens equation and the equation for magnification. By solving for the image distance using the thin-lens equation, the image height can then be calculated using the magnification factor. It is important to ensure that all units are consistent in order for the equations to work accurately. Drawing a ray diagram can also help in visualizing the result.
  • #1
map7s
146
0
A camera with a focal length f of 6 cm is used to take the picture of a person who is 180 cm tall, standing at a distance 3 m in front of the camera.
How big will the image of that person be on film?
How far behind the lens (assumed to be very thin) must the film be placed?


I tried using the thin-lens equation and the equation of magnification, but I can't seem to be getting the right answer.

(1/d o)+(1/d i)=(1/f)
m=-(d i)/(d o)

Using the first equation, I plugged in the numbers for f and d o and solved for d i. I know that there is something special with the signs, but I tried them every way possible, and I still can't get the right answer.
 
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  • #2
Show more of your calculation, and what answer it came to.
 
  • #3
In order to solve for d i : (1/6)-(-1/3)=1/d i -> d i =2
m=2/-3
 
  • #4
map7s said:
In order to solve for d i : (1/6)-(-1/3)=1/d i -> d i =2
m=2/-3

Be careful of your units. f is in centimeters, and the object distance is in meters! They need to be consistent for the equation to work.
I'm not sure why you have -1/3. Why did you pick negative?
 
Last edited:
  • #5
okay, that was what was messing me up - the units. But is there anything special that you have to do for part a of the problem? b/c I tried using the equation for magnification. I got part b right, so I took that answer and divided by 300. (m = - (d i)/(d o)
 
  • #6
If you know how to draw a ray diagram you could try doing that. The numbers in the question are quite round so you should be able to get quite an accurate answer from drawing a ray diagram.
 
  • #7
I only know how to draw a ray diagram without using numbers (like the image appears on the opposite side of the lens inverted and smaller, but I wouldn't be able to tell how much smaller).
 
  • #8
Magnification is also expressed as M = (image height)/(object height).

So you've already found the magnification factor. Now apply the above ratio to find the image height, since you also know the height of the person in the picture.
 

1. How do camera lenses affect the size of objects in a photograph?

Camera lenses play a significant role in how objects appear in a photograph. The focal length of the lens determines the magnification of the objects, with shorter focal lengths resulting in a wider field of view and larger objects, and longer focal lengths resulting in a narrower field of view and smaller objects.

2. Can I use any type of lens to capture different object sizes?

Yes, different lenses can be used to capture different object sizes. Wide-angle lenses are ideal for capturing large objects or landscapes, while telephoto lenses are better for capturing small objects or distant subjects.

3. How does the distance between the camera and the object affect its size in the photograph?

The distance between the camera and the object can have a significant impact on its size in the photograph. The closer the object is to the camera, the larger it will appear in the photo. On the other hand, increasing the distance between the camera and the object will result in a smaller size in the photo.

4. Does the aperture of the lens affect the size of objects in a photograph?

Yes, the aperture of the lens can also affect the size of objects in a photograph. A wider aperture (lower f-stop) will result in a shallower depth of field, causing the object to appear larger compared to the background. On the other hand, a smaller aperture (higher f-stop) will result in a larger depth of field, making the object appear smaller in relation to the background.

5. How can I calculate the size of an object in a photograph using optics?

To calculate the size of an object in a photograph, you need to know the focal length of the lens, the distance between the camera and the object, and the distance between the object and the background. By using the lens equation and the magnification formula, you can determine the size of the object in relation to the actual size. It is important to note that this calculation may vary depending on the type of lens and camera being used.

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