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JEE Advance - Physics (2022 - Paper 1 Online - No. 12)

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 $\theta$ 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?

The ray of light will come out for $\theta=30^{\circ}$, for $0< l < L$.
There is an angle for $l=\frac{L}{2}$ at which the ray of light will come out after two reflections.
The ray of light will NEVER come out for $\theta=60^{\circ}$, and $l=\frac{L}{3}$.
The ray of light will come out for $\theta=60^{\circ}$, and $0 < l < \frac{L}{2}$ after six reflections.

Explanation

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

As we can see, for $$\theta=30^\circ$$, the ray will incident normally and hence will retrace its path.

$$\Rightarrow$$ (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

$$\Rightarrow$$ (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.

$$\Rightarrow$$ (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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