Convex mirrors are curved mirrors that bulge outward, and they have some unique properties:

1. Image Characteristics for Convex Mirrors:

   • Convex mirrors always produce images with the following characteristics:
     • Location: The image is located behind the convex mirror.
     • Type: It’s a virtual image (meaning it cannot be projected onto a screen).
     • Orientation: The image is upright (not inverted).
     • Size: The image is reduced in size compared to the object.

2. Mirror Equation:

   • The mirror equation relates the object distance ((d_o)), image distance ((d_i)), and focal length ((f)): [ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} ]
   • For example, if you have a 4.0 cm tall light bulb placed 35.5 cm from a convex mirror with a focal length of -12.2 cm:
     • Given: (h_o = 4.0 , \text{cm}), (d_o = 35.5 , \text{cm}), and (f = -12.2 , \text{cm})
     • Solve for (d_i): [ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} ] [ -0.0820 , \text{cm}^{-1} = 0.0282 , \text{cm}^{-1} + \frac{1}{d_i} ] [ d_i = -9.08 , \text{cm} ]

3. Determine Focal Length:

   • If an image is 16.0 cm behind a convex mirror when the object is 28.5 cm from the mirror, we can find the focal length:
     • Given: (d_i = 16.0 , \text{cm}) and (d_o = 28.5 , \text{cm})
     • Use the mirror equation: [ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} ] [ \frac{1}{f} = \frac{1}{28.5 , \text{cm}} + \frac{1}{16.0 , \text{cm}} ] [ f = -36.6 , \text{cm} ]