Two mirrors are inclined at an angle θ as shown in the diagram. Light ray is incident parallel to one of the mirrors. The ray will start retracting its path after third reflection if:

Question

Two mirrors are inclined at an angle θ as shown in the diagram. Light ray is incident parallel to one of the mirrors. The ray will start retracting its path after third reflection if: <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-3lou47lmj4z2hiqc.jpg" /> (A) θ = 4 5°  (B) θ = 3 0°  (C) θ = 6 0°  (D) All three

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-3lou47lmj4z2cple.jpg" /> α =((9 0 - θ )/2),(α )1=90-α and also, (α )1 = 9 0 - θ = 9 0 - ((9 0 - θ /2)) 9 0 - θ = 4 5 + (θ /2) 4 5 = (3 θ /2) θ = 3 0°

Q. Two mirrors are inclined at an angle $θ$ as shown in the diagram. Light ray is incident parallel to one of the mirrors. The ray will start retracting its path after third reflection if :

$θ = 4 5^{\circ}$

$θ = 3 0^{\circ}$

$θ = 6 0^{\circ}$

All three

$α = \frac{( 90 - θ )}{2}, (α)_{1} = 90 - α$ and also,
$(α)^{1} = 90 - θ = 90 - (\frac{90 - θ}{2})$
$90 - θ = 45 + \frac{θ}{2}$
$45 = \frac{3 θ}{2}$
$θ = 3 0^{\circ}$

Q. Two mirrors are inclined at an angle θ as shown in the diagram. Light ray is incident parallel to one of the mirrors. The ray will start retracting its path after third reflection if :

θ=45∘

θ=30∘

θ=60∘