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 .

Question

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" /> (A)  tan -1(0.75) (B)  cot -1(0.75) (C)  sin -1(0.75) (D)  cos -1(0.75)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-pe6ealuiqjejnoi9.jpg" /> The situation shown in the figure tanθ =(2 x/a)=(a - x/y)=(a/a - y) On solving cotθ =(3/4) ⇒ cot -1(0.75)

Q. $A B, BC, C D$ and $D A$ are identical mirror used to from a square as shown in the figure(Top view). A ray starting from the midpoint $M$ of $A D$ undergoes two reflections before reaching the corner $D$ . Find angle $θ$ .

$tan^{- 1} (0.75)$

$cot^{- 1} (0.75)$

$sin^{- 1} (0.75)$

$cos^{- 1} (0.75)$

The situation shown in the figure
$t an θ = \frac{2 x}{a} = \frac{a - x}{y} = \frac{a}{a - y}$
On solving
$co tθ = \frac{3}{4}$
$\Rightarrow cot^{- 1} (0.75)$

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 θ .

tan−1(0.75)

cot−1(0.75)

sin−1(0.75)

cos−1(0.75)