13. An object is 9 cm from a convex mirror that has a focal length of 5 cm . Determine the image location, magnification, real or virtual, and upright or inverted for the object. a. Using the equation:

To find the image location, we can use the mirror formula: \( \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \), where \( f \) is the focal length (positive for convex mirrors), \( u \) is the object distance (negative for convex mirrors), and \( v \) is the image distance. Plugging in the values, we have: \( f = +5 \) cm, \( u = -9 \) cm. Rearranging gives us \( \frac{1}{v} = \frac{1}{f} - \frac{1}{u} \), or \( \frac{1}{v} = \frac{1}{5} - \frac{1}{-9} \). Calculating gives \( v = +3.17 \) cm. The positive value indicates that the image is formed on the same side as the object. Next, to find magnification \( m \), we use: \( m = -\frac{v}{u} \). Substituting \( v = 3.17 \) cm and \( u = -9 \) cm gives \( m = -\frac{3.17}{-9} = 0.35 \). The positive magnification means the image is upright. Thus, the image is virtual, upright, and reduced in size. --- Convex mirrors are fascinating! Historically, they were used in ancient times for personal grooming and have evolved into essential tools for road safety, providing wider angles of view to reduce blind spots. Every time you see a convex mirror on a shopkeeper's counter or on a vehicle, you’re witnessing their incredible utility! For a practical problem-solving tip, always remember to keep track of your sign conventions: object distance (u) should be negative for concave and convex mirrors, while the focal length (f) is positive for convex mirrors. Not adhering to these can lead to mix-ups in signs and errors in calculating the image distance and magnification!