Final answer:
The distance from the lens to the film in a camera with a 35.0 mm focal length lens, when photographing a flower 75.0 cm away, is approximately 3.66 cm.
Step-by-step explanation:
In order to find the distance from the lens to the film, we can use the lens equation which states that 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the distance of the object from the lens, and u is the distance of the image from the lens. In this case, the focal length is 35.0 mm and the object distance is 75.0 cm.
We can convert the object distance to meters by dividing by 100, so v = 0.75 m.
Assuming that the image distance u is positive (since it is on the same side as the object), we can solve for u using the lens equation:
1/35.0 mm = 1/0.75 m - 1/u
Rearranging the equation, we have:
1/u = 1/0.75 m - 1/35.0 mm
Converting the focal length to meters, we have:
1/u = 1/0.75 m - 1/0.035 m
Calculating the right side of the equation gives:
1/u = 1.333 m-1 - 28.571 m-1
1/u = -27.238 m-1
Taking the reciprocal, we find that u = -0.0366 m.
Since the image distance is negative, it means that the image is located on the same side as the object, which is to the left of the lens. Therefore, the distance from the lens to the film is the absolute value of the image distance, which is 0.0366 m or 3.66 cm.