Question

Four identical mirrors are made to stand vertically to from a square arrangement as shown in a top view. A ray start from the midpoint M of mirror AD and after two reflection reaches corner D. Then angle $\theta$ must be:

• A. $\tan ^ { - 1 } ( 0.75 )$
• B. $\cot ^ { - 1 } ( 0.75 )$
• C. $\sin ^ { - 1 } ( 0.75 )$
• D. $\cos ^ { - 1 } ( 0.75 )$

Answer 1

Answer: (B)

$\cot ^ { - 1 } ( 0.75 )$

Answer 2

:

The ray starting from point M at an angle $\theta$ reaches the corner D at the right along a parallel path. Let a be the length of the side.

From figure,

$\tan \theta = \frac { x } { ( a / 2 ) }$ …(i)

…(ii)

…(iii)

From (i) and (ii), we get

$\frac { 2 x } { a } = \frac { a - x } { y }$

$2 x y = a ^ { 2 } - x a$

From (ii) and (iii), we get …(iv)

$\frac { a - x } { y } = \frac { a } { a - y }$

$3 x y = 2 a y$ (Using (iv))

Substituting this value of x in equation (i), we get