An object is 10 cm from a concave mirror that has a focal length of 5 cm . Determine image location, magnification, real or virtual, and upright or inverted for the object. a. Using the equation:

To determine the image location, magnification, whether the image is real or virtual, and whether it is upright or inverted for an object placed in front of a concave mirror, we can use the mirror equation: \[ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \] where: - \( f \) is the focal length of the mirror, - \( d_o \) is the distance of the object from the mirror, - \( d_i \) is the distance of the image from the mirror. Given: - Focal length (\( f \)) = 5 cm - Distance of the object from the mirror (\( d_o \)) = 10 cm Let's calculate the image location (\( d_i \)) using the mirror equation. Calculate the value by following steps: - step0: Calculate: \(\frac{1}{5}-\frac{1}{10}\) - step1: Reduce fractions to a common denominator: \(\frac{2}{5\times 2}-\frac{1}{10}\) - step2: Multiply the numbers: \(\frac{2}{10}-\frac{1}{10}\) - step3: Transform the expression: \(\frac{2-1}{10}\) - step4: Subtract the numbers: \(\frac{1}{10}\) The image location (\( d_i \)) is 10 cm from the mirror. Now, let's calculate the magnification (\( M \)) using the formula: \[ M = -\frac{d_i}{d_o} \] where: - \( M \) is the magnification, - \( d_i \) is the distance of the image from the mirror, - \( d_o \) is the distance of the object from the mirror. Given: - Distance of the object from the mirror (\( d_o \)) = 10 cm - Distance of the image from the mirror (\( d_i \)) = 10 cm Let's calculate the magnification (\( M \)). Calculate the value by following steps: - step0: Calculate: \(\frac{-10}{10}\) - step1: Reduce the fraction: \(-1\) The magnification (\( M \)) is -1. Since the magnification is negative, the image is inverted. Therefore, the image location is 10 cm from the mirror, the magnification is -1, the image is real, and it is inverted.