Question Detail
Question
An object is placed 30 cm in front of a concave mirror of radius of curvature 20 cm. Determine the characteristics of its image.
Correct Answer
Option A is the correct answer.
Detailed Explanation
f = R/2 = 10 cm. u = -30 cm. 1/f = 1/u + 1/v => 1/10 = 1/(-30) + 1/v => 1/v = 1/10 + 1/30 = 4/30 = 2/15 => v = 15/2 = 7.5 cm. The image is real (v positive), inverted, and since v < u, it's diminished. Magnification m = -v/u = -7.5/-30 = 0.25. So it's diminished. The image distance is 7.5 cm from the pole. None of the options have 7.5 cm. Let's re-check. 1/v = 1/10 - 1/30 = 2/30 = 1/15 => v = 15 cm. m = -15/-30 = 0.5. So the image is inverted, diminished, and 15 cm from the pole. Option A matches.
Hint
Use the mirror equation and magnification formula.