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Two plane mirrors are inclined at an angle such that a ray incident on one mirror undergoes a total deviation of 240 degrees after two successive reflections. Which of the following statements is/are correct? (A) The angle between the mirrors is 60 degrees. (B) If an object is placed symmetrically between the mirrors, the number of images formed is 5. (C) If an object is placed unsymmetrically between the mirrors, the number of images formed is 5. (D) A ray will retrace its path after 2 successive reflections if the angle of incidence on the first mirror is 60 degrees.

1. A and B only
2. A, B and C only
3. A, C and D only
4. B, C and D only

Correct answer: A, B and C only

Solution

(A) Total deviation = 360 - 2*theta = 240 → theta = 60 degrees. TRUE. (B) 360/60 = 6 (even integer). Number of images for symmetric placement = 6-1 = 5. TRUE. (C) When 360/theta = even integer (here 6), the number of images is 5 regardless of symmetric or unsymmetric placement. TRUE. (D) For a ray to retrace its path, total deviation must be 180 degrees, requiring theta = 90 degrees. Since theta = 60 degrees here, retro-reflection does not occur regardless of the angle of incidence. FALSE.

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