Q5. A concave mirror has a radius of curvature 12 cm. At what distance from the mirror should an object be placed to give a virtual image three times the object size?

Step 1: Calculate the focal length of the concave mirror. The focal length f of a spherical mirror is half its radius of curvature R. f = (R)/(2) Given R = 12 cm. f = 12 cm2 f = 6 cm For a concave mirror, the focal length is considered positive in the mirror formula. Step 2: Determine the magnification and relate image distance to object distance. The image is virtual and three times the object size. For a virtual image, the magnification m is positive. m = +3 The magnification formula is m = -(v)/(u), where v is the image distance and u is the object distance. 3 = -(v)/(u) v = -3u The negative sign for v indicates that the image is virtual and formed behind the mirror. Step 3: Apply the mirror formula. The mirror formula is (1)/(f) = (1)/(u) + (1)/(v). Substitute f = 6 cm and v = -3u into the formula. (1)/(6 cm) = (1)/(u) + (1)/(-3u) (1)/(6 cm) = (1)/(u) - (1)/(3u) Step 4: Solve for the object distance u. To combine the terms on the right side, find a common denominator, which is 3u. (1)/(6 cm) = (3)/(3u) - (1)/(3u) (1)/(6 cm) = (3 - 1)/(3u) (1)/(6 cm) = (2)/(3u) Cross-multiply to solve for u. 3u = 2 × 6 cm 3u = 12 cm u = 12 cm3 u = 4 cm The object should be placed at a distance of 4 cm from the mirror. That's 2 down. 3 left today — send the next one.