Physics: Reflection of LIght

Question

A basketball player of height 2.60 m is standing 2.90 m in front of a convex spherical mirror of radius of curvature 3.00 m. Determine the size of the image.

Im confused on how to solve this without knowing the distance from the focal point? The answer with an explanation would be appreciated!

Answer 1

p = object distance = 2.90 m

q = image distance = ?

h = object height = 2.60 m

R = radius of curvature = 3.00 m

f = focal length = -R/2 = -3.00/2 m = -1.5 m (focal length of convex mirror is negative)

M = magnification = -q/p

h_i = image height = Mh = ?

 

1/p + 1/q = 1/f = -2/R

 

1/2.90 + 1/q = -2/3.00

 

q = 1/(-2/3.00 - 1/2.90) m ≅ -0.9886 m

 

M = -q/p = -(-0.9886)/2.90 ≅ 0.3409

 

Image is virtual, upright, and shrunken.

 

h_i = Mh = 0.3409(2.60) m ≅ 0.886 m