The mirror equation, which establishes a relationship between object distance \( u \), image distance \( v \), and focal length \( f \) of a mirror, is given by: \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] The following values are provided: - \( f = -10 \, \text{cm} \) (focal length of the concave mirror; negative as it is concave), - \( u = -15 \, \text{cm} \) (object distance; negative as the object is in front of the mirror), - \( v \) represents the image distance, which needs to be calculated. To find \( v \), the mirror equation is rearranged as follows: \[ \frac{1}{v} = \frac{1}{f} - \frac{1}{u} \] Substituting the known values yields: \[ \frac{1}{v} = \frac{1}{-10} - \frac{1}{-15} \] \[ \frac{1}{v} = -\frac{1}{10} + \frac{1}{15} = -\frac{3}{30} + \frac{2}{30} = -\frac{1}{30} \] Consequently, the image distance is: \[ v = -30 \, \text{cm} \] The negative sign for \( v \) indicates that the image is formed on the same side as the object, signifying a real and inverted image. The image is located \( 30 \, \text{cm} \) from the mirror.