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 the sign convention. For a convex mirror: The object is placed in front of the mirror, so the object distance u is negative. u = -15 cm The image formed by a convex mirror is always virtual and formed behind the mirror, so the image distance v is positive. v = +5 cm Step 2: Use the mirror formula. The mirror formula is given by: (1)/(f) = (1)/(v) + (1)/(u) where f is the focal length. Step 3: Substitute the values into the mirror formula and solve for f. (1)/(f) = (1)/(5 cm) + (1)/(-15 cm) (1)/(f) = (1)/(5 cm) - (1)/(15 cm) To subtract the fractions, find a common denominator, which is 15. (1)/(f) = (3)/(15 cm) - (1)/(15 cm) (1)/(f) = (3 - 1)/(15 cm) (1)/(f) = (2)/(15 cm) Now, invert both sides to find f: f = 15 cm2 f = 7.5 cm The focal length of the convex mirror is 7.5 cm.