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: Calculate the focal length (f) of the concave mirror. The radius of curvature (R) is given as 36 \, cm. For a concave mirror, the focal length is half the radius of curvature: f = (R)/(2) f = 36 \, cm2 f = 18 \, cm For a concave mirror, the focal length is positive. Step 2: Determine the magnification (M). The problem states that a real image is formed, which is three times the size of the object. For a real image formed by a concave mirror, the image is always inverted. Therefore, the magnification is negative. M = -3 Step 3: Use the magnification formula to relate image distance (v) and object distance (u). The magnification formula for mirrors is: M = -(v)/(u) Substitute the value of M: -3 = -(v)/(u) v = 3u Since u (object distance) is always positive for a real object, v (image distance) is also positive, which is consistent with a real image formed in front of the mirror. Step 4: Use the mirror formula to solve for the object distance (u). The mirror formula is: (1)/(f) = (1)/(u) + (1)/(v) Substitute f = 18 \, cm and v = 3u into the mirror formula: (1)/(18) = (1)/(u) + (1)/(3u) To combine the terms on the right side, find a common denominator, which is 3u: (1)/(18) = (3)/(3u) + (1)/(3u) (1)/(18) = (3+1)/(3u) (1)/(18) = (4)/(3u) Now, cross-multiply to solve for u: 3u = 4 × 18 3u = 72 u = (72)/(3) u = 24 \, cm The object should be placed at a distance of 24 \, cm from the mirror. The object distance is 24 cm.