Question

The owner of a van installs a rear-window lens that has a focal length of -0.340 m. When the owner looks out through the lens at an object located directly behind the van, the object appears to be 0.240 m from the back of the van, and appears to be 0.390 m tall. (a) How far from the van is the object actually located, and (b) how tall is the object?

Answer 1

Answer:

0.816 m

1.326 m

Explanation:

u = Object distance

v = Image distance = -0.24

f = Focal length = -3 m (concave lens)

$h_v$ = Image height = 0.39 m

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\\\Rightarrow \frac{1}{-0.34}=\frac{1}{u}+\frac{1}{-0.24}\\\Rightarrow \frac{1}{u}=\dfrac{1}{-0.34}+\dfrac{1}{0.24}\\\Rightarrow u=0.816\ m$

The object is 0.816 m from the van

$m=\frac{h_v}{h_u}\\\Rightarrow -\frac{v}{u}=\frac{h_v}{h_u}\\\Rightarrow h_u=-\dfrac{h_vu}{v}\\\Rightarrow h_u=-\dfrac{0.39\times 0.816}{-0.24}\\\Rightarrow h_u=1.326\ m$

The height of the object is 1.326 m