Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • . A glass prism of refractive index is immersed in water <img alt="\left(\mu=\frac{4}{3}\right)" src="https://entran

. A glass prism of refractive index 1.5 is immersed in water \left(\mu=\frac{4}{3}\right). A light beam incident normally on the face \mathrm{AB} is totally reflected to reach the face \mathrm{BC} if:

Option: 1

\mathrm{\sin \theta \leq \frac{2}{3}}


Option: 2

\mathrm{\cos \theta \geq \frac{8}{9}}


Option: 3

\mathrm{\sin \theta\geq \frac{8}{9}}


Option: 4

\mathrm{\cos \leq \frac{8}{9}}


Answers (1)

best_answer

\mathrm{Here, { }^{\mathrm{a}} \mu_{\mathrm{g}}=1.5=\frac{3}{2},{ }^{\mathrm{a}} \mu_{\mathrm{w}}=\frac{4}{3} } \\ \mathrm{{ }^w \mu_g \times{ }^w \mu_g={ }^a \mu_g}
\mathrm{\therefore \quad{ }^w \mu_g=\frac{{ }^a \mu_g}{{ }^a \mu_w}=\frac{3 / 2}{4 / 3}=\frac{9}{8}}
\mathrm{\begin{aligned} & \mathrm{\text { As } \sin C=\frac{1}{{ }^w \mu_g}=\frac{1}{9 / 8}=\frac{8}{9}} \\ & \mathrm{C=\sin ^{-1}\left(\frac{8}{9}\right)} \end{aligned}}
For total internal reflection, \mathrm{\theta>C}
\mathrm{\theta>\sin ^{-1}\left(\frac{8}{9}\right) \text { or } \sin \theta\geq \frac{8}{9}}

Posted by

Pankaj

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026 Registration LIVE: NTA session 1 applications close on November 27; apply at jeemain.nta.nic.in
anam-khan

JEE 2026: IIT admissions show major shift toward AI, data science, away from core engineering courses
anam-khan

JEE Main 2026: NIT Delhi cut-offs for BTech courses show ever-increasing demands for AI, computer skills

Latest Question