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Geometrical Optics question

2003 · Shift 0 · Q141
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Geometrical Optics question

2003 · Shift 0 · Q141

JEE MainPhysicsGeometrical OpticsMCQ+4 / −1
To get three images of a single object, one should have two plane mirrors at an angle of
  1. A
    60∘{60^ \circ }60∘
  2. B
    90∘{90^ \circ }90∘
  3. C
    120∘{120^ \circ }120∘
  4. D
    30∘{30^ \circ }30∘
View written solutionFree

Correct answer: B

  1. For two plane mirrors inclined at an angle θ\thetaθ, the number of images formed is given by
N=360∘θ−1N = \frac{360^\circ}{\theta} - 1N=θ360∘​−1

when 360∘θ\dfrac{360^\circ}{\theta}θ360∘​ is an integer.

  1. We need N=3N = 3N=3 images.

So,

360∘θ−1=3\frac{360^\circ}{\theta} - 1 = 3θ360∘​−1=3 360∘θ=4\frac{360^\circ}{\theta} = 4θ360∘​=4 θ=360∘4=90∘\theta = \frac{360^\circ}{4} = 90^\circθ=4360∘​=90∘
  1. Now check the options:
  • A: 60∘⇒N=36060−1=560^\circ \Rightarrow N = \frac{360}{60} - 1 = 560∘⇒N=60360​−1=5
  • B: 90∘⇒N=36090−1=390^\circ \Rightarrow N = \frac{360}{90} - 1 = 390∘⇒N=90360​−1=3
  • C: 120∘⇒N=360120−1=2120^\circ \Rightarrow N = \frac{360}{120} - 1 = 2120∘⇒N=120360​−1=2
  • D: 30∘⇒N=36030−1=1130^\circ \Rightarrow N = \frac{360}{30} - 1 = 1130∘⇒N=30360​−1=11

Thus, the required angle is

90∘\boxed{90^\circ}90∘​

So the correct option is B.

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