Solveeit Logo
Login

Question

Question: A glass prism of refractive index 1.5 is immersed in water \(( \mu = 4 / 3 )\). A light beam inciden...

A glass prism of refractive index 1.5 is immersed in water (μ=4/3)( \mu = 4 / 3 ). A light beam incident normally on the face AB is totally reflected to reach the face BC if

A

sin⁡θ>8/9\sin \theta > 8 / 9

B

2/3<sin⁡θ<8/92 / 3 < \sin \theta < 8 / 9

C

sin⁡θ≤2/3\sin \theta \leq 2 / 3

D

cos⁡θ≥8/9\cos \theta \geq 8 / 9

Answer

sin⁡θ>8/9\sin \theta > 8 / 9

Explanation

Solution

From figure it is clear that

Total internal reflection takes place at AC, only if θ > C

⇒sin⁡θ>sin⁡C\Rightarrow \sin \theta > \sin C

⇒sin⁡θ>1ωμg\Rightarrow \sin \theta > \frac { 1 } { { } _ { \omega } \mu _ { g } }

⇒sin⁡θ>89\Rightarrow \sin \theta > \frac { 8 } { 9 }