A rectangle ABCD is kept in front of a concave mirror of focal length f with its corners A and B being, respectively, at distances 2f and 3f from the mirror with AB along the principal axis as shown in the figure. It forms an image A'B'C'D' in front of the mirror. What is the ratio of B'C' to A'D'?

  1. A. 1
  2. B. 2
  3. C. \frac{1}{2} ✓
  4. D. \frac{2}{3}

Correct Answer: C. \frac{1}{2}

Explanation

For corner A at u = -2f, image is at v = -2f with magnification -1. For B at u = -3f, using mirror formula, v = -1.5f with magnification -0.5. The ratio of heights (B'C' to A'D') is the ratio of their magnifications, which is 0.5 / 1 = 1/2.

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