A glass prism (μ=1.5) is dipped in water (μ=4 / 3) as shown in figure. A light ray is incident normally on the surface A B. It reaches the surface B C after totally reflected, if

Question

A glass prism (μ=1.5) is dipped in water (μ=4 / 3) as shown in figure. A light ray is incident normally on the surface A B. It reaches the surface B C after totally reflected, if (A)  sin θ ≥ 8 / 9 (B) 2 / 3 < sin θ < 8 / 9 (C)  sin θ ≤ 2 / 3 (D) It is not possible

Tardigrade Admin · Accepted Answer

For TIR at A C <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/73114cd83fe84d28edc972f6199e1185-.png" /> θ > C ⇒ sin θ ≥ sin C ⇒ sin θ ≥ (1/ w μg) ⇒ sin θ ≥ (μw/μg) ⇒ sin θ ≥ (8/9)

Q. A glass prism $(μ = 1.5)$ is dipped in water $(μ = 4/3)$ as shown in figure. A light ray is incident normally on the surface $A B$ . It reaches the surface $BC$ after totally reflected, if

$sin θ \geq 8/9$

$2/3 < sin θ < 8/9$

$sin θ \leq 2/3$

It is not possible

For TIR at $A C$

$θ > C$
$\Rightarrow sin θ \geq sin C$
$\Rightarrow sin θ \geq \frac{1}{_{w} μ _{g}}$
$\Rightarrow sin θ \geq \frac{μ _{w}}{μ _{g}}$
$\Rightarrow sin θ \geq \frac{8}{9}$

Q. A glass prism (μ=1.5) is dipped in water (μ=4/3) as shown in figure. A light ray is incident normally on the surface AB. It reaches the surface BC after totally reflected, if

sinθ≥8/9

2/3<sinθ<8/9

sinθ≤2/3