Question

The owner of a van installs a rear-window lens that has a focal length of -0.299 m. When the owner looks out through the lens at a person standing directly behind the van, the person appears to be just 0.241 m from the back of the van, and appears to be 0.335 m tall.

(a) How far from the van is the person actually standing?
m

(b) How tall is the person?
m

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 = 1/0.241 - 1/0.299

1/S1 = 0.80489

S1 = 1.19 m

Person is 1.24 m behind the van
------- ------- ------- -------- --------- ---------

Same equation for height:

1H1 = 1/0.335 - 1/0.299

H1 = 1/(-0.3594)

= -2.78, which is 2.78m inverted

Person is 2.78 m tall