A convex mirror in an amusement park has a radius of curvature of 3.00 m. 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?
2007-12-01 15:50:34 · 1 answers · asked by Abc 3 in Science & Mathematics ➔ Physics
The answer is 2.25 actually, but i dont know how to get there.
2007-12-02 03:20:38 · update #1
The lens / mirror equation is
1 / f = 1 / di + 1 / do
where f is the focal length, di the image distance, and do the object distance.
The magnification m is
m = - di / do
You want m = 1/2 so
1/2 = -di / do
do = -2 di
The focal length of your mirror is half the radius of curvature. The mirror is convex, so the focal length is negative.
f = - 1.50 m
Put it all together...
1 / f = 1 / di + 1 / do
1 / ( -1.50 ) = 1 / di - 1 / 2di
- 2 / 3 = 2 / 2di - 1 / 2di
-2 / 3 = 1 / 2di
di = ( 1 / 2 ) ( -3 / 2 ) = - 3 / 4 m
The image distance is -.75 m. The negative sign means that the image is virtual and on the opposite side of the mirror as the man.
2007-12-01 17:13:11 · answer #1 · answered by jgoulden 7 · 0⤊ 1⤋