The height of the image is 2.55 cm.
When an object is placed on the optical axis of a convex spherical mirror, the mirror equation relates the object distance (u), the image distance (v), and the focal length (f) of the mirror. The mirror equation is given by:
1/f= 1/v+ 1/u
Given the focal length of the convex spherical mirror as f=51 cm, an object height (h obj) of 2.0 cm, and the object distance (u) as 80 cm, we can use this equation to find the image distance (v).
Solving for v, we find v≈102 cm. The magnification (m) can be determined using the magnification formula,
m=− v/u, which results in m≈−1.275. The negative sign indicates that the image is inverted.
The height of the image (h img) can be found using the magnification relationship:
h img=m×h obj. Substituting the values, we get h img≈−2.55 cm. Taking the absolute value, the height of the image is approximately 2.55 cm.