Pdf of a camera with telephoto lens of focal length 125 mm takes a picture of 1.8m tall woman standing 5.0m away.
(1).what is the magnification of the image
(2). What's the size of the woman's image on the film
To find the magnification of the image produced by the camera with a telephoto lens, we can use the magnification formula:
Magnification = (Size of the image)/(Size of the object)
Before we can calculate the magnification, we need to find the size of the image and the size of the object.
1. Calculate the size of the image:
We know that the woman's height is 1.8m. To find the size of the image, we need to determine the height of the image captured by the camera's lens.
Given that the camera is 5.0m away from the woman, and it has a telephoto lens with a focal length of 125mm (0.125m), we can use the lens formula:
1/f = 1/u + 1/v
Where:
f = focal length of the lens
u = object distance
v = image distance
Plugging in the values:
1/0.125 = 1/5 + 1/v
Simplifying the equation:
8 = 1 + 0.125/v
7 = 0.125/v
v = 0.125/7
v ≈ 0.0179m
This value represents the distance from the lens to the image on the film (also known as the "image distance").
Now we can calculate the size of the image using the equation:
Size of the image = Size of the object * (v/u)
Plugging in the values:
Size of the image = 1.8 * (0.0179/5)
Size of the image ≈ 0.0065m
So, the size of the woman's image on the film is approximately 0.0065m.
2. Calculate the magnification:
Using the formula:
Magnification = (Size of the image)/(Size of the object)
Plugging in the values:
Magnification = 0.0065/1.8
Magnification ≈ 0.0036
Therefore, the magnification of the image is approximately 0.0036.