A building is to be photographed with a camera. The distance to the building is

Question

A building is to be photographed with a camera. The distance to the building is 160m, the building's height is 95m and the width is 50m. You can choose between 35mm, 50mm, 135mm and 250mm lenses (focal length of the lenses). Select the lens that gives the largest image of the building (the entire building will be included in the movie). The film has a frame of 24mm × 36mm.
a) What lens do you choose? [mm]
b) How big is the image of the building? Reply with rounded integers. Answer both the width [mm] and height [mm].
c) How big is the distance between the lens and the film? Assume that the thickness of the lens is negligible. Answer with two decimal for this answer [mm].

Explanation / Answer

object distance s = 160 m

for lens f = 35 mm = 0.035 m

1/s + 1/s' = 1/f

1/160 + 1/s' = 1/0.035

s' = 0.035 m = 35 mm

h'/h = s'/s

h'/95 = 35/160

h' = 21 mm

-----------------------------

object distance s = 160 m

for lens f = 50 mm = 0.050 m

1/s + 1/s' = 1/f

1/160 + 1/s' = 1/0.05

s' = 0.05 m = 50 mm

h'/h = s'/s

h'/95 = 50/160

h' = 30 mm

------------------

for lens f = 135 mm = 0.135 m

1/s + 1/s' = 1/f

1/160 + 1/s' = 1/0.135

s' = 0.135 m = 135 mm

h'/h = s'/s

h'/95 = 135/160

h' = 80 mm

==================

(a)

50 mm

=================

(b)

height h' = 30 mm

width = 50*(50/160) = 16 mm

===================

(c)

image distance = 50 mm

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