A common zoom lens for a digital camera covers a focal length of 18 mm to 200 mm

Question

A common zoom lens for a digital camera covers a focal length of 18 mm to 200 mm. For the purposes of this problem, treat the lens as a thing lens. If the lens is zoomed out to 200 mm and is focused on a petroglyph that is 15 m away and 38 cm wide, (a) how far is the lens from the photosensor array of the camera and (b) how wide is the image of the petroglyph on the sensors? (c) If the closest that the lens can get to the senesors at its 18 mm focal length is 5.2 cm, what is the closest object it can focus on at that focal length?

Explanation / Answer

Part A)
Apply 1/f = 1/p + 1/q

1/.2 = 1/15 + 1/q

q = .203 m (20.3 cm)

Part B)
h'/h = -q/p

h'/38 = -.203/15

h' = -.514 cm or -5.14 mm (Negative just means inverted)

Part C)

1/1.8 = 1/p + 1/5.2

p = 2.75 cm

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