A 35 mm camera using a standard 50.0 mm lens is focused on a 1.80 m tall person

Question

A 35 mm camera using a standard 50.0 mm lens is focused on a 1.80 m tall person who is standing 3.25 m from the lens. You now refocus the camera on a 15.0 cm tall flower that is 75.0 cm from the lens. (a) In refocusing, by how much did you move the lens? Did you move it toward the film or away from it? (b) What is the height of the flower%u2019s image on the film?

I know the answers are: lens moves 2.8mm away from the film. The image of the flower is 10.7mm tall, but I'm not sure why. Also if you could explain what the 35 mm is used for in this problem I would really appreciate it.

Explanation / Answer

a) This part they are asking for the image distance. Use the thin lens equation to find the image distance.

1/p + 1/q = 1/f

p=the distance from Carlos to the camera = 3000mm
f=focal length = 50mm

1/3000 + 1/q = 1/50

q = 50.847mm

b) magnification = -image distance (q) / object distance (p)
= -50.847/3000
= -.0169 X
c) the height of Carlos on the film is his height multiplied by the magnification.

= 1200mm * .0169
= 20.28mm

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