Final answer:
Using the mirror equation and magnification formula, we can find the height of the image formed by a convex spherical mirror. By plugging in the given values and following the steps, we can calculate a height of approximately 14.07 cm for the image.
Step-by-step explanation:
To find the height of the image formed by a convex spherical mirror, we can use the mirror equation:
1/f = 1/do + 1/di
Where f is the focal length of the mirror, do is the distance of the object from the mirror, and di is the distance of the image from the mirror. In this case, the focal length is 51 cm, the object distance is 80 cm, and we want to find the image distance (di). Rearranging the equation, we get:
1/di = 1/f - 1/do
Plugging in the values, we have:
1/di = 1/51 - 1/80
Simplifying, we find:
1/di = (80 - 51) / (51 * 80) = 29 / (51 * 80) = 29 / 4080 = 1/140.6897
Taking the reciprocal of both sides gives us:
di = 140.6897 cm
Therefore, the height of the image can be found using the magnification formula:
magnification = -di/do
Using the values, we have:
magnification = -140.6897/80 = -1.7586
Since magnification is defined as the ratio of the height of the image to the height of the object, we can calculate the height of the image by multiplying the magnification by the height of the object:
height of the image = -1.7586 * 8.0 cm = -14.0696 cm
Therefore, the height of the image is approximately 14.07 cm.