A convex mirror is a type of spherical mirror that curves outward. When light rays strike a convex mirror, they diverge (spread out). Here are some key points about convex mirrors:

1. Mirror Equation:

   • The mirror equation relates the object distance ((d_o)), image distance ((d_i)), and focal length ((f)).
   • It’s expressed as:

     f1​=do​1​+di​1​

2. Sign Conventions:

   • Object distance ((d_o)) is positive when the object is in front of the mirror.
   • Image distance ((d_i)) is positive when the image is formed on the same side as the object.
   • Focal length ((f)) is positive for convex mirrors.

3. Example Problem:

   • Let’s say we have a 4.0 cm tall light bulb placed 35.5 cm from a convex mirror with a focal length of -12.2 cm.
   • We want to determine the image distance and image size.
   • Using the mirror equation:
     • (\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i})
     • Substituting known values:
       • (\frac{1}{-12.2 , \text{cm}} = \frac{1}{35.5 , \text{cm}} + \frac{1}{d_i})
       • Solving for (d_i):
         • (d_i = -9.08 , \text{cm})
   • The image distance is approximately -9.08 cm.
   • To find the image height ((h_i)), we use the magnification equation:
     • (\frac{h_i}{h_o} = -\frac{d_i}{d_o})
     • Substituting known values:
       • (\frac{h_i}{4.0 , \text{cm}} = -\frac{-9.08 , \text{cm}}{35.5 , \text{cm}})
       • Solving for (h_i):
         • (h_i \approx 7.5 , \text{cm})