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
Welcome back — missed you this week. Step 1: Identify the given values and apply sign conventions. The object is placed in front of a convex mirror. Object distance, u = 2 m. According to the Cartesian sign convention, for a real object, u is negative. So, u = -2 m. Magnification, m = (1)/(3). For a convex mirror, the image is always virtual and erect, so the magnification is positive. We need to find the focal length, f. For a convex mirror, the focal length f is positive. Step 2: Calculate the image distance (v) using the magnification formula. The magnification formula for mirrors is: m = -(v)/(u) Substitute the known values: (1)/(3) = -(v)/(-2) (1)/(3) = (v)/(2) Multiply both sides by 2 to solve for v: v = (2)/(3) m The positive value of v indicates that the image is virtual and formed behind the mirror, which is consistent with a convex mirror. Step 3: Calculate the focal length (f) using the mirror formula. The mirror formula is: (1)/(f) = (1)/(u) + (1)/(v) Substitute the values of u and v: (1)/(f) = (1)/(-2) + (1)/(2)3 (1)/(f) = -(1)/(2) + (3)/(2) Combine the fractions: (1)/(f) = (-1 + 3)/(2) (1)/(f) = (2)/(2) (1)/(f) = 1 f = 1 m The positive value of f is consistent with the focal length of a convex mirror. The focal length of the mirror is 1 m. Send me the next one 📸