A glass prism of refractive index 1.5 is A immersed in water of refractive index (4/3.) A light incident normally on the face AB is totally reflected to reach the face AC, if :

Question

A glass prism of refractive index 1.5 is A immersed in water of refractive index (4/3.) A light incident normally on the face AB is totally reflected to reach the face AC, if : (A)  sin θ >(3/2)  (B)  sin θ >(2/3)  (C)  sin θ >(8/9)  (D)  (2/3) sin θ >(8/9)

Tardigrade Admin · Accepted Answer

Key Idea: There will be total internal reflection at face AC.
The critical angle is the angle of incidence I the denser medium for which the angle of refraction in the rarer medium is

9 0^{\circ} .

From Snells law

_{g} n_{w} = \frac{s i n C}{s i n 90 ^{o}}

\Rightarrow

sin C = \frac{_{a} n _{w}}{_{a} n _{g}} = \frac{4/3}{1.5}

= \frac{8}{9}

For total internal reflection

θ > C

.

∴ sin θ > \frac{8}{9}

.

Q. A glass prism of refractive index $1.5$ is $A$ immersed in water of refractive index $\frac{4}{3.}$ A light incident normally on the face $A B$ is totally reflected to reach the face $A C$ , if :

$sin θ > \frac{3}{2}$

$sin θ > \frac{2}{3}$

$sin θ > \frac{8}{9}$

$\frac{2}{3} sin θ > \frac{8}{9}$

Q. A glass prism of refractive index 1.5 is A immersed in water of refractive index 3.4​ A light incident normally on the face AB is totally reflected to reach the face AC, if :

sinθ>23​

sinθ>32​

sinθ>98​

32​sinθ>98​

Q. A glass prism of refractive index $1.5$ is $A$ immersed in water of refractive index $\frac{4}{3.}$ A light incident normally on the face $A B$ is totally reflected to reach the face $A C$ , if :

$sin θ > \frac{3}{2}$

$sin θ > \frac{2}{3}$

$sin θ > \frac{8}{9}$

$\frac{2}{3} sin θ > \frac{8}{9}$