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QJEEAdv22Phb58f: JEE Advanced 2022 Physics - Class 12 JEEAdv22Phb58f Solution: Three plane mirrors form an equilateral triangle with each side …

Three plane mirrors form an equilateral triangle with each side of length LL . There is a small hole at a distance l>0 from one of the corners as shown in the figure. A ray of light is passed through the hole at an angle θ\theta and can only come out through the same hole. The cross section of the mirror configuration and the ray of light lie on the same plane.

JEE Advanced 2022 Paper 1 Online Physics - Geometrical Optics Question 18 English

Which of the following statement(s) is(are) correct?

Multiple Choice Options

  • A The ray of light will come out for θ=30∘\theta=30^{\circ} , for 0<l<L0< l < L .
  • B There is an angle for l=L2l=\frac{L}{2} at which the ray of light will come out after two reflections.
  • C The ray of light will NEVER come out for θ=60∘\theta=60^{\circ} , and l=L3l=\frac{L}{3} .
  • D The ray of light will come out for θ=60∘\theta=60^{\circ} , and 0<l<L20 < l < \frac{L}{2} after six reflections.

Step-by-Step Verified Solution

JEE Advanced 2022 Paper 1 Online Physics - Geometrical Optics Question 18 English Explanation 1

As we can see, for θ=30∘, the ray will incident normally and hence will retrace its path.

⇒ (A) is correct

Considering the symmetry of the situation, we can have :

JEE Advanced 2022 Paper 1 Online Physics - Geometrical Optics Question 18 English Explanation 2

⇒ (B) is correct

JEE Advanced 2022 Paper 1 Online Physics - Geometrical Optics Question 18 English Explanation 3

As is clear from the above diagram, ray comes out.

⇒ (C) is not correct

Also, as is clear from the above diagram, total number of reflections = 5.

(D) is not correct.

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