A convex mirror has a focal length of 20 cm. Determine the object location for which the image will be one half as tall as the object.
2007-03-11 14:26:43 · 1 answers · asked by Kitana 2 in Science & Mathematics ➔ Physics
The mirror equation expresses the quantitative relationship between the object distance (do), the image distance (di), and the focal length (f). The equation is stated as follows:
1/f = 1/do +1/di =================1
The Magnification equation relates the ratio of the image distance (di) and object distance (do) to the ratio of the image height (hi) and object height (ho). The magnification equation is stated as follows:
M = hi /ho = - di/do
These two equations can be combined to yield information about the image distance and image height if the object distance, object height, and focal length are known.
Multiplying equation 1 by di.
di /f = di /do + 1.
It is given that hi /ho = ½
Therefore, M = hi /ho = - di/do = 1/2
di/do = - ½ = 0.5
f = - 20 cm.
- di /20 = - 0.5 +1 = 0.5
- di = 10cm
di = - 10cm
The negative value for image distance indicates that the image is located behind the mirror.
From di/do = - ½
do = 20cm.
The object is in front of the mirror.
2007-03-11 15:05:41 · answer #1 · answered by Pearlsawme 7 · 0⤊ 0⤋