Question

The owner of a van installs a rear-window lens that has a focal length of -0.350 m. When the owner looks out through the lens at an object located directly behind the van, the object appears to be 0.220 m from the back of the van, and appears to be 0.310 m tall. (a) How far from the van is the object actually located, and (b) how tall is the object?

Answer 1

With a thin lens:

1/S1 + 1/S2 = 1/f, where S1 is the distance of the person behind the van to the lens, S2 is the distance of the van owner's eyes to the lens, and f is the focal length of the lens

1/S1 = -1/S2 + 1/f

1/S1 = 1/0.220 - 1/0.350

1/S1 = 1.68

S1 = 0.59 m

Person is 0.59 m behind the van
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Same equation for height:

1H1 = 1/0.310 - 1/0.350

H1 = 1/(-0.368)

= -2.71, which is 2.71 m inverted

Person is 2.64 m tall