You want to take a full length photo of your friend who is 2 m tall, using a 35 mm camera having a 50 mm lens. The image dimensions of 35 mm film is 24 mm by 36 mm, and you want to make this a vertical photo in which your friend's image completely fills the image area. (a) How far should your friend stand from the lens? (b) How far is the lens from the film?
ok.. I am confused..help please!
Sure! I can help you with that. Let's break it down into two parts:
a) How far should your friend stand from the lens?
To calculate this, we need to use similar triangles. The height of your friend is 2 m, and the height of the image on the film is 36 mm. We want to find the distance your friend should stand from the lens (let's call this distance "x").
Using the properties of similar triangles, we can set up the following proportion:
2 m / x = 36 mm / 24 mm
To solve for x, we can cross-multiply and then divide:
2 m * 24 mm = 36 mm * x
48 m * mm = 36 mm * x
48 (m * mm) / (36 mm) = x
Simplifying the units gives us:
(48/36) m = x
4/3 m = x
So, your friend should stand approximately 1.33 meters away from the lens.
b) How far is the lens from the film?
Since we want the image to completely fill the image area of the film, the lens-to-film distance should be equal to the lens-to-subject distance.
So, the distance between the lens and the film should also be approximately 1.33 meters.
I hope that helps! Let me know if you have any more questions.
No worries, I can help clarify the steps you need to take to figure out the answers to your questions!
To determine how far your friend should stand from the lens, we can use the concept of similar triangles. Here's how:
(a) How far should your friend stand from the lens?
1. First, let's find the proportion between your friend's height and the image height:
- Your friend's height: 2 m
- Image height: 36 mm (as per the dimensions of the film)
2. Since the image will completely fill the vertical area of the film, the height of your friend's image should be equal to the height of the film.
3. Set up a proportion to solve for the distance your friend should stand from the lens:
- Friend's height / Friend's distance = Image height / Lens-to-film distance
Substitute the known values:
- 2 m / Friend's distance = 36 mm / Lens-to-film distance
4. Convert the units to keep things consistent:
- 2 m = 2000 mm (since there are 1000 mm in a meter)
5. Rearrange the equation to solve for Friend's distance:
- Friend's distance = (Image height * Friend's distance) / Image height
- Friend's distance = (36 mm * 2000 mm) / 2 m
This calculation will give you the distance your friend should stand from the lens.
(b) How far is the lens from the film?
To find the distance between the lens and the film, we can use the lens formula, which is:
1/Focal Length = 1/Object Distance + 1/Image Distance
Since the friend's height completely fills the image, the image distance will be equal to the focal length.
Substituting the values we know:
1/50 mm = 1/Object Distance + 1/Film Distance
Since we already calculated the Object Distance (Friend's distance), we can substitute that as well:
1/50 mm = 1/Friend's Distance + 1/Film Distance
Now, rearrange the equation to solve for the Film Distance:
1/Film Distance = 1/50 mm - 1/Friend's Distance
Film Distance = 1 / (1/50 mm - 1/Friend's Distance)
By calculating the reciprocal of the right-hand side, you can find the value of the Film Distance.
Please remember to convert the units to the same scale (mm) for accurate results.
(a) The magnification ratio 2.0/0.036 = 55.56, tells you the do/di ratio.
You also know that
1/do + 1/di = 1/0.050 m = 20 m^-1
Solve for do
1/do + 55.56/do = 56.56/do = 20
do = 2.83 m
di = 2.83/55.56 = 0.0509m = 50.9 mm