Question

If a 9 cm dia. ornament is hanging from a tree and the reflection in the ornament is 1/2 the size, how far away is the person viewing it?

Answer 1

@IrishBoy123

Answer 2

@Michele_Laino

Answer 3

Oh, I think this ends up being just a simple 1/f= 1/do + 1/di problem, right?

Answer 4

yes it does

Answer 5

eg look at qu3 on this
http://www.physics.louisville.edu/sbmendes/phys%20222%20spring%2012/quizzes/answers%20quiz%209.pdf

Answer 6

so f = -2.25, i think.......

Answer 7

we have to consider the formula of magnification

Answer 8

Right, thanks so much!

Answer 9

for example, if we write this:
\[\frac{1}{p} + \frac{1}{q} = \frac{1}{f}\]
where \(p\) is the distance of the object and \(q\) is the distance of the image, then the magnification \(G\) is given by the subsequent formula:
\[G = \frac{q}{p}\]

Answer 10

In your case, since the magnification is equal to 2, then we can write:
\[G = \frac{q}{p} = 2 \Rightarrow q = 2p\]

Answer 11

so we get:
\[\frac{1}{p} + \frac{1}{q} = \frac{1}{f} \Rightarrow \frac{1}{p} + \frac{1}{{2p}} = \frac{4}{D}\]
where \(D= 9\) cm, please solve that equation for \(p\)

Answer 12

Hm, where did the 4 come from?

Answer 13

half of half of diameter is focal length...

Answer 14

correct! @IrishBoy123 we can write this:
\[f = \frac{R}{2} = \frac{{D/2}}{2} = \frac{D}{4} \Rightarrow \frac{1}{f} = \frac{4}{D}\]