If incident ray MP and reflected ray QN are parallel to each other, find the angle θ between the mirrors.

Question

If incident ray MP and reflected ray QN are parallel to each other, find the angle θ between the mirrors. (A) 60° (B) 45° (C) 90° (D) 180°

Tardigrade Admin · Accepted Answer

The deviation produced by first mirror =180-2 i1 and the deviation produced by second mirror =180-2 i 2 The total deviation is 180° as MP and Q N are anti parallel So, 180°=360°-2( i 1+ i 2) ∴ i 1+ i 2=θ=90°

Q. If incident ray MP and reflected ray QN are parallel to each other, find the angle $θ$ between the mirrors.

$6 0^{\circ}$

$4 5^{\circ}$

$9 0^{\circ}$

$18 0^{\circ}$

The deviation produced by first mirror $= 180 - 2 i_{1}$
and the deviation produced by second mirror $= 180 - 2 i_{2}$
The total deviation is $18 0^{\circ}$ as MP and $QN$ are anti parallel
So, $18 0^{\circ} = 36 0^{\circ} - 2 (i_{1} + i_{2})$
$∴ i_{1} + i_{2} = θ = 9 0^{\circ}$

Q. If incident ray MP and reflected ray QN are parallel to each other, find the angle θ between the mirrors.

60∘

45∘

90∘

180∘