Q48 / 54 · JEE Advanced 2022 (Paper 1) · Physics

Three plane mirrors form an equilateral triangle with each side of length L. 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 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.

Figure

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

  • Correct answer
    A
    The ray of light will come out for θ=30°, for 0<l<L.
  • Correct answer
    B
    There is an angle for l=L2 at which the ray of light will come out after two reflections.
  • C
    The ray of light will NEVER come out for θ=60°, and l=L3.
  • D
    The ray of light will come out for θ=60°, and 0<l<L2 after six reflections.

Solution

Figure

As we can see, for θ=30°, the ray will incident normally and hence will retrace its path, hence the ray will come out for θ=30° and 0<l<L.

⇒A is correct

Considering the symmetry of the situation, we can have:

Figure

Thus, for θ=60° and l=L2, ray will come out from the setup after two reflections.

⇒B is correct

Now, when θ=60° and l=L3, the ray on entering the setup will suffer five reflections and eventually will come out.

Figure

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.

Hence, the correct answer is options: 'A', 'B'.

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