# Optics hi/ho formula

1. Dec 14, 2005

### unctarheels1

In the following problem, I am having trouble understanding the components.

- The image of a man just covers the length of a 5cm plane mirror when the mirror is held vertically 30cm from the eye. The tree is 100m from the mirror. What is the height?

* To find the height you would use hi/ho = -i/o
and you would also use 1/i + 1/o = 1/f to find these components. But I can not understand what the measurements mean in the question.

The object would be the tree, 100m from the mirror.
What are the other two (5cm and 30 cm)

Can I use the hi/ho formula directly for this problem?

2. Dec 14, 2005

### Astronuc

Staff Emeritus
Is there more information, such as the height of the man, or does the tree image span the same mirror held at 30 cm from the eye? If 'man' was 'tree' the problem would make more sense.

Maybe I am missing something.

3. Dec 14, 2005

### unctarheels1

The man is the tree, I was thinking about something else when I typed it in.

4. Dec 14, 2005

### Astronuc

Staff Emeritus
Since it is a plane mirror, one wound not use 1/i + 1/o = 1/f, or rather 1/f = 0.

Think about looking through a plane of glass at the same tree. The image at 30 cm is 5 cm high, whereas the actual object is 100 m from the observer.

Draw a triangle with a leg 5 cm high at 30 cm (0.3 m) along the base from the vertex (observer). Then extend to a similar triangle along the base 100 m.

Now with respect to the mirror, if the tree is 100 m, behind the observer (vertical plane through eye), then the image of the tree would 0.3 m (from observer to mirror, and 100.3 m from mirror to tree).