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  4. AB,BC,CD and DA are identical mirror used to from a square as shown in the figure(Top view). A ray starting from the midpoint M of AD undergoes two reflections before reaching the corner D . Find angle θ . <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-pe6ealuiqjej4api.jpg />

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Q. $AB,BC,CD$ and $DA$ are identical mirror used to from a square as shown in the figure(Top view). A ray starting from the midpoint $M$ of $AD$ undergoes two reflections before reaching the corner $D$ . Find angle $\theta $ .
Question

NTA AbhyasNTA Abhyas 2022

Solution:

Solution
The situation shown in the figure
$tan\theta =\frac{2 x}{a}=\frac{a \, - \, x}{y}=\frac{a}{a \, - \, y}$
On solving
$cot\theta =\frac{3}{4}$
$\Rightarrow \cot ^{-1}(0.75)$