A glass prism ABC (refractive index 1.5), immersed in water (refractive index (4/3) ). A ray of light is incident normally one face AB. If it is totally reflected at the face AC, then

Question

A glass prism ABC (refractive index 1.5), immersed in water (refractive index (4/3) ). A ray of light is incident normally one face AB. If it is totally reflected at the face AC, then <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-1ec2gu7wjyzw.png" /> (A) sinθ ≥ (8/9) (B) sinθ ≥ (2/3) (C) sinθ ≥ (√3/2) (D) (2/3) < sinθ < (8/9)

Tardigrade Admin · Accepted Answer

For total internal reflection at face AC sinθ >(μ w/μ g) ⇒ sinθ ≥ (4/3 × 1.5) ⇒ sinθ ≥ (8/9)

Q. A glass prism $A BC$ (refractive index 1.5), immersed in water (refractive index $\frac{4}{3}$ ). A ray of light is incident normally one face $A B .$ If it is totally reflected at the face $A C,$ then

$s in θ \geq \frac{8}{9}$

$s in θ \geq \frac{2}{3}$

$s in θ \geq \frac{3}{2}$

$\frac{2}{3} < s in θ < \frac{8}{9}$

For total internal reflection at face $A C$
$s in θ > \frac{μ _{w}}{μ _{g}}$
$\Rightarrow s in θ \geq \frac{4}{3 \times 1.5}$
$\Rightarrow s in θ \geq \frac{8}{9}$

Q. A glass prism ABC (refractive index 1.5), immersed in water (refractive index 34​ ). A ray of light is incident normally one face AB. If it is totally reflected at the face AC, then

sinθ≥98​

sinθ≥32​

sinθ≥23​​

32​<sinθ<98​