Question

The owner of a van installs a rear-window lens that has a focal length of -0.298 m. When the owner looks out through the lens at a person standing directly behind the van, the person appears to be just 0.245 m from the back of the van, and appears to be 0.338 m tall. (a) How far from the van is the object actually located, and (b) how tall is the object?

Answer 1

a) 1.376 m

b) 1.899 m

Step-by-step explanation:

Given

Focal length of the lens, f = -0.298 m

Distance of the image, d(i) = 0.245 m

Size of the image, I = 0.338 m

Using the following connotations,

O = object size

do = object distance

I = image size

di = image distance

f = focal length

The owner has a concave lens.

The magnification of this lens is I/O = (-f + di)/-f

I/O = (0.298 - 0.245)/0.298 =

I/O = 0.053 / 0.298

I/O = 0.178

Also,

I/O = -di/do, so that

I/O = 0.178 = -di/do

do = 0.245/0.178 = 1.376 m (distance of person from rear of car.

O = I/0.178

O = 0.338/0.178

O = 1.899 m (size of person)

Therefore, the distance of the object from the van is 1.376 m and the size of the object is 1.899 m