A monochromatic beam of light enters a square enclosure with mirrored interior surfaces at an angle of incidence \theta_i (≠0) (see the figure below). For some value(s) of \theta_i , the beam is reflected by every mirrored wall (other than the one with the opening) exactly once and exits the enclosure through the same hole. Which of the following statements about this beam is correct?

Correct Answer is : The beam will come out only at θi=45°

The beam will not come out of the enclosure for any value of \theta_i

The beam will come out for more than two values of \theta_i

The beam will come out only at \theta_i = 45^\circ

The beam will come out for exactly two values of \theta_i

KVPY 2020-21 SA Exam Previous Papers

Question : 30 of 80

Marks: +1, -0

A monochromatic beam of light enters a square enclosure with mirrored interior surfaces at an angle of incidence

θ_i

(≠0) (see the figure below). For some value(s) of

θ_i

, the beam is reflected by every mirrored wall (other than the one with the opening) exactly once and exits the enclosure through the same hole. Which of the following statements about this beam is correct?

The beam will not come out of the enclosure for any value of $θ_i$
The beam will come out for more than two values of $θ_i$
The beam will come out only at $θ_i = 45°$
The beam will come out for exactly two values of $θ_i$

Validate

Solution:

As per the drawn diagram the ray comes out from square e =

θ_i

From above ray diagram by symmetry, the reflected rays form rhombus and inside the square it will be square
(as per basic symmetry)

{e}=\θ_{i}

2 \θ_{i}=90°

\θ_{i}=45°

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