Final answer:
Using the lens formula, we can determine the film distance from a 50.0 mm focal length lens for a subject 3.00 m away, the fraction of a 1.75 m tall person that fits on 36.0 mm high film, and discuss the reasonableness based on photography experience.
Step-by-step explanation:
Calculations Using Lens Formula
To solve these problems, we'll use the lens formula, which is
1/f = 1/do + 1/di, where
f is the focal length,
do is the object distance, and
di is the image distance from the lens.
(a) Let's find how far from the lens the film must be when using a
50.0 mm focal length lens to photograph a person 3.00 m (3000 mm) away. We can rearrange the lens formula to solve for di:
d
i
= 1/(1/f - 1/d
o
)
(b) To determine what fraction of a 1.75 m tall person will fit on a 36.0 mm high film, we use the concept of similar triangles. The ratio of the object's height to the object's distance (from the lens) is the same as the ratio of the image's height to the image's distance (from the lens).
Image height on film / Image distance from lens = Object height / Object distance
(c) In personal experience, the fraction calculated for a 1.75 m tall person fitting into 36.0 mm high film seems reasonable judging by similar scenarios in photography, as long the lens and film specification allow it.