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Concepts Of Physics MCQ Edition [Volume 1]PhysicsOptical Instruments

A person observes several trees in an open space, with the following details given. Arrange the trees in decreasing order of their apparent sizes. Tree Height (m) Distance from the eye (m) A 2.0 50 B 2.5 80 C 1.8 70 D 2.8 100

Options

  1. AB , A , C , D
  2. BA , D , B , C
  3. CC , D , B , A
  4. DA , B , D , C

Correct answer

D. A , B , D , C

Step-by-step solution

The apparent size of an object is proportional to the visual angle it subtends at the eye. For small angles, this angle is given by h d , where h is the height of the object and d is its distance from the eye. Calculating the visual angle for each tree: For tree A: _A = 2.0 50 = 0.040 rad For tree B: _B = 2.5 80 = 0.03125 rad For tree C: _C = 1.8 70 0.0257 rad For tree D: _D = 2.8 100 = 0.028 rad Comparing the angles, we get _A > _B > _D > _C . The decreasing order of their apparent sizes is A, B, D, C.

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