A convex mirror in an amusement park has a radius of curvature of 3.00m. A man stands in front of the mirror so that his image is half as tall as his actual height. At what distance must the man focus his eyes in order to see his image?

I calculated the focal length using f=(-.5)(3.00m)

then I tried to find the image distance(di) but I get stuck.

What am I supposed to be doing here?

you kind of just droped 1/di there. where did it go?

I just don't get how you got to:

1/di - 1/2di

and then you went from

1/di - 1/2di = 1/2di.....you just droped 1/di. That doesnt make any since.

you all calculating rubbish

You have correctly determined that f = -1.5 m for this mirror. From the magnification of 1/2, and the fact that it is a virtual image, you also know that

di/do = -1/2.

Therefore 1/di + 1/do = 1/di - 1/2di =
1/2di = 1/f = -2/3

Therefore di = -3/2 m and do = 3 m

Since the observer is the "object" and his image is on the other side of the mirror, he must focus his eyes 4.5 meters away.

Check my thinking. I could have made a mistake somewhere

1/di could also be written 2/2di then if you take away 1/2di you are left with 1/2di. It's like saying 1 minus 1/2 equals 1/2

To find the image distance (di) in this case, you can use the mirror formula:

1/f = 1/do + 1/di

where f is the focal length of the mirror, do is the object distance (distance of the man from the mirror), and di is the image distance (distance of the image from the mirror).

Given that the focal length (f) is -(0.5)(3.00m), you correctly calculated that.

Next, you need to find the object distance (do). The question states that the man's image is half as tall as his actual height. This means the height of the image (hi) is half the height of the man (ho). Let's assume the height of the man is h.

Then, hi = 0.5 * ho
And, hi/ho = 0.5

Now, using the mirror equation for a convex mirror, we have:

hi/ho = -di/do

Substituting -di/do = 0.5 into the equation, we can solve for do:

-0.5 = -di/do
do = 2di

Using this relationship, we can determine that the object distance (do) is twice the image distance (di).

Now, we know the relationship between do and di. We need to find both do and di.

To find di, we can use the mirror formula again:

1/f = 1/do + 1/di

Replacing do with 2di:

1/f = 1/(2di) + 1/di

Simplifying the equation, we get:

1/f = 3/(2di)

Rearranging the formula to solve for di:

di = (2f)/3

By substituting the value of f (-(0.5)(3.00m)), you can calculate the value of di:

di = (2 * (-(0.5)(3.00m)))/3

Solving this equation will give you the value of di, which is the distance at which the man must focus his eyes to see his image.