A camera with a telephoto lens of focal length 125mm takes a picture of a 1.8m tall woman standing 5.0m away.
(1). What must be the distance between the film and the lens to get a properly focused picture?
(2). What is the magnification of the image
(3). What is the size of the woman's image on the film?
To answer these questions, we can use the thin lens formula:
1/f = 1/u + 1/v
where f is the focal length of the lens, u is the object distance, and v is the image distance.
1. To find the distance between the film and the lens (v), we need to find the image distance. In this case, the object distance (u) is 5.0m, and the focal length (f) is 125mm. Converting the focal length to meters (125mm = 0.125m), we can plug in the values into the thin lens formula:
1/0.125 = 1/5 + 1/v
Simplifying the equation:
8 = 0.2 + 1/v
Rearranging the equation:
1/v = 8 - 0.2
1/v = 7.8
v = 1/7.8 ≈ 0.128m
Therefore, the distance between the film and the lens to get a properly focused picture is approximately 0.128 meters.
2. The magnification of the image (M) can be calculated using the formula:
M = -v/u
Plugging in the values:
M = -0.128/5
M ≈ -0.0256
The negative sign indicates that the image is inverted compared to the object. The magnification is approximately -0.0256.
3. Lastly, to find the size of the woman's image on the film, we can use the magnification formula:
M = h'/h
where h' is the size of the image and h is the size of the object.
In this case, we know that the height of the woman (h) is 1.8m. Rearranging the formula:
h' = M * h
h' = -0.0256 * 1.8
h' ≈ -0.04608
The negative sign again indicates that the image is inverted. The size of the woman's image on the film is approximately -0.04608 meters.