Provided Information:
Focal length (\( f = 15 \, \text{cm} \))
Object distance (\( u = -30 \, \text{cm} \), indicating a real object)
Procedure:
Step 1: Apply the Mirror Formula The governing equation is: \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] with \( f \) representing focal length, \( v \) representing image distance, and \( u \) representing object distance.
Step 2: Calculate Image Distance (\( v \)) Substitute the given values: \[ \frac{1}{15} = \frac{1}{v} + \frac{1}{-30} \] Rearranging the equation: \[ \frac{1}{v} = \frac{1}{15} + \frac{1}{30} \] Combine the fractions: \[ \frac{1}{v} = \frac{2}{30} + \frac{1}{30} = \frac{3}{30} = \frac{1}{10} \] Therefore, the image distance is: \[ v = 10 \, \text{cm} \]
Conclusion: The calculated image distance is 10 cm. The provided answer option (c) stating 60 cm is incorrect based on the calculations.