WAEC 2024 Physics · Question 5

An object 2.0 cm high is placed at the radius of curvature of a concave mirror such that it is perpendicular…

Question

An object 2.0 cm high is placed at the radius of curvature of a concave mirror such that it is perpendicular to the principal axis of the mirror. Determine the height of the image.

A.0.5 cm
B.1.0 cm
C.1.5 cm
D.2.0 cm

Answer: D. 2.0 cm

Explanation written with AI and checked against the answer key

Analyze the question: The object is placed at the radius of curvature (u = R = 2f) of a concave mirror. We need the image height. Concept: The mirror formula is 1/f = 1/u + 1/v, and magnification is m = v/u = h_i/h_o (ignoring the sign, which only tells us the image is inverted). Solution: Since the object is at the radius of curvature, u = R = 2f. 1/v = 1/f − 1/u 1/v = 1/f − 1/(2f) 1/v = (2 − 1)/(2f) = 1/(2f) So v = 2f, which means the image forms at the centre of curvature too. Magnification: m = v/u = 2f/2f = 1 Image height: h_i = m × h_o = 1 × 2.0 cm = 2.0 cm Nature of the image: real, inverted, and the same size as the object, located at C (the centre of curvature). Answer: The image height is 2.0 cm, which is option D. Exam tip: Remember the special case for a concave mirror: when the object is at C (2f), the image is at C, real, inverted, and the same size (m = 1). Whenever a question says "placed at the radius of curvature," think "same size." The image height will equal the object height.

AI can make mistakes. Report anything that looks wrong.