The focal length of your camera lens is 70mm. It is used for taking pictures of your friend who is 1.5m tall. What is your friends distance from the lens if the image just fills the 24mm vertical dimension of the film?
I tried M=hi/ho=.16
.16=di-f/f di=-68.88
Careful. 1.5 m is 15000 mm.
.016=di-f/f = 71.12
.016=-di/d0 =4.445m
1.5m=1500mm
To solve this problem, you can use the thin lens equation and the magnification equation.
First, let's label the given information:
Focal length (f) = 70mm
Height of your friend (ho) = 1.5m
Height of the image (hi) = 24mm
Now let's use the thin lens equation:
1/f = 1/di - 1/do
Since the image fills the 24mm vertical dimension of the film, we know the image distance (di) is equal to the focal length (f):
di = f = 70mm
Now, let's use the magnification equation:
M = hi / ho = -di / do
To find the object distance (do), we need to rearrange the magnification equation:
do = -di / (M * ho)
Plugging in the given values:
do = -70mm / (24mm / (1.5m)) [Note: Convert ho from meters to millimeters by multiplying by 1000]
do = -70mm / (24mm / 1500)
do = -70mm / 0.016mm
do = -4375mm
The distance of your friend from the lens is approximately 4375mm (or -4.375m) when the image just fills the 24mm vertical dimension of the film. The negative sign indicates that the object is in front of the lens.