Question

1. photography elizabeth has a camera in which the distance from the lens to the film is 24 millimeters.

a. if elizabeth takes a full - length photograph of her friend from a distance of 3 meters and the height of her friend is 140 centimeters, what will be the height of the image on the film? (hint: convert to the same unit of measure.)
b. suppose the height of the image on the film of her friend is 15 millimeters. if francine took a full - length shot, what was the distance between the camera and her friend

Explanation:

Step1: Convert units to centimeters

Friend's height: $140$ cm, distance: $3$ m $= 300$ cm, lens-to-film: $24$ mm $= 2.4$ cm

Step2: Set up proportion for similar triangles

$\frac{\text{Image height}}{\text{Friend's height}} = \frac{\text{Lens-to-film}}{\text{Distance to friend}}$
$\frac{x}{140} = \frac{2.4}{300}$

Step3: Solve for image height (a)

$x = 140 \times \frac{2.4}{300}$
$x = 1.12$

Step4: Set up proportion for part (b)

$\frac{\text{Image height}}{\text{Friend's height}} = \frac{\text{Lens-to-film}}{\text{Distance to friend}}$
$\frac{1.5}{140} = \frac{2.4}{d}$

Step5: Solve for distance (b)

$d = 140 \times \frac{2.4}{1.5}$
$d = 224$

Answer:

a. 1.12 centimeters
b. 224 centimeters (or 2.24 meters)