This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the given values and apply sign conventions. The object is placed in front of a convex mirror. Object distance, u = 20 cm. According to the Cartesian sign convention, for a real object, u is negative. So, u = -20 cm. Focal length, f = 20 cm. For a convex mirror, the focal length f is positive. So, f = +20 cm. We need to determine the distance between the object and its image. Step 2: Calculate the image distance (v) using the mirror formula. The mirror formula is: (1)/(f) = (1)/(u) + (1)/(v) Substitute the known values: (1)/(20) = (1)/(-20) + (1)/(v) To solve for (1)/(v), rearrange the equation: (1)/(v) = (1)/(20) - (1)/(-20) (1)/(v) = (1)/(20) + (1)/(20) (1)/(v) = (1+1)/(20) (1)/(v) = (2)/(20) (1)/(v) = (1)/(10) v = 10 cm The positive value of v indicates that the image is virtual and formed 10 cm behind the mirror. Step 3: Calculate the distance between the object and its image. The object is located 20 cm in front of the mirror (u = -20 cm). The image is located 10 cm behind the mirror (v = +10 cm). Since the object and image are on opposite sides of the mirror, the distance between them is the sum of their absolute distances from the mirror. Distance between object and image = |u| + |v| Distance between object and image = |-20 cm| + |10 cm| Distance between object and image = 20 cm + 10 cm Distance between object and image = 30 cm The distance between the object and its image is 30 cm. That's 2 down. 3 left today — send the next one.