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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Optical Instruments

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Optical Instruments

A person observes several trees in an open space, with the...

A person observes several trees in an open space, with the following details given. Arrange the trees in decreasing order of their apparent sizes.
TreeHeight (m)Distance from the eye (m)
A2.02.05050
B2.52.58080
C1.81.87070
D2.82.8100100

Options

  1. ABB, AA, CC, DD
  2. BAA, DD, BB, CC
  3. CCC, DD, BB, AA
  4. DAA, BB, DD, CC

Correct answer

D. AA, BB, DD, CC

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 θ≈hd\theta \approx \dfrac{h}{d}, where hh is the height of the object and dd is its distance from the eye.

Calculating the visual angle for each tree:

For tree A: θA=2.050=0.040\theta_A = \dfrac{2.0}{50} = 0.040 rad

For tree B: θB=2.580=0.03125\theta_B = \dfrac{2.5}{80} = 0.03125 rad

For tree C: θC=1.870≈0.0257\theta_C = \dfrac{1.8}{70} \approx 0.0257 rad

For tree D: θD=2.8100=0.028\theta_D = \dfrac{2.8}{100} = 0.028 rad

Comparing the angles, we get θA>θB>θD>θC\theta_A > \theta_B > \theta_D > \theta_C.

The decreasing order of their apparent sizes is A, B, D, C.
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