A ray of light entering from air into a denser medium of refractive index $\frac{4}{3}$, as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle $\theta$ should be equal to :
$\sin ^{-1} \frac{\sqrt{7}}{3}$
$\sin ^{-1} \frac{\sqrt{5}}{4}$
$\sin ^{-1} \frac{\sqrt{7}}{4}$
$\sin ^{-1} \frac{\sqrt{5}}{3}$
Correct Option: 1
At maximum angle $\theta$ ray at point B goes in gazing emergence, at all less values of $\theta$, TIR occurs.
At point B
$\frac{4}{3} \times \sin \theta^{\prime \prime}=1 \times \sin 90^{\circ}$
$\theta^{\prime \prime}=\sin ^{-1}\left(\frac{3}{4}\right)$
$\theta^{\prime}=\left(\frac{\pi}{2}-\theta^{\prime \prime}\right)$
At point $\mathrm{A}$
$1 \times \sin \theta=\frac{4}{3} \times \sin \theta^{\prime}$
$\sin \theta=\frac{4}{3} \times \sin \left(\frac{\pi}{2}-\theta^{\prime \prime}\right)$
$\sin \theta=\frac{4}{3} \cos \left[\cos ^{-1} \frac{\sqrt{7}}{4}\right]$
$\sin \theta=\frac{4}{3} \times \frac{\sqrt{7}}{4}$
$\theta=\sin ^{-1}\left(\frac{\sqrt{7}}{3}\right)$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,