Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced 2024Paper 1
Exam
JEE Advanced
Year
2024
Paper
Paper 1
Subject
Physics
Chapter
Ray Optics

JEE Advanced 2024 · Paper 1 · Physics · Ray Optics

A light ray is incident on the surface of a sphere of refractive...

A light ray is incident on the surface of a sphere of refractive index nn at an angle of incidence θ0\theta_0. The ray partially refracts into the sphere with angle of refraction ϕ0\phi_0 and then partly reflects from the back surface. The reflected ray then emerges out of the sphere after a partial refraction. The total angle of deviation of the emergent ray with respect to the incident ray is α\alpha. Match the quantities mentioned in List-I with their values in List-II and choose the correct option. A light ray is incident on the surface of a sphere of refractive index n at an angle of incidence θ_0 . The ray

Options

  1. AP→5;Q→2;R→1;S→4\mathrm{P} \rightarrow 5 ; \mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 1 ; \mathrm{S} \rightarrow 4
  2. BP→5;Q→1;R→2;S→4\mathrm{P} \rightarrow 5 ; \mathrm{Q} \rightarrow 1 ; \mathrm{R} \rightarrow 2 ; \mathrm{S} \rightarrow 4
  3. CP→3;Q→2;R→1;S→4\mathrm{P} \rightarrow 3 ; \mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 1 ; \mathrm{S} \rightarrow 4
  4. DP→3;Q→1;R→2;S→5\mathrm{P} \rightarrow 3 ; \mathrm{Q} \rightarrow 1 ; \mathrm{R} \rightarrow 2 ; \mathrm{S} \rightarrow 5

Correct answer

A. P→5;Q→2;R→1;S→4\mathrm{P} \rightarrow 5 ; \mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 1 ; \mathrm{S} \rightarrow 4

Step-by-step solution

α=(θ0−ϕ0)+(180−2ϕ0)+(θ0−2ϕ0)α=180+2θ0−4ϕ0\begin{aligned} & \alpha=\left(\theta_0-\phi_0\right)+\left(180-2 \phi_0\right)+\left(\theta_0-2 \phi_0\right) \\ & \alpha=180+2 \theta_0-4 \phi_0\end{aligned}\textbf{(P) } \alpha=180+2 \theta_0-4 \phi_0 180=180+2 \theta_0-4 \phi_0 \Rightarrow \theta_0=2 \phi_0...(i)...(i)\sin \theta_0=2 \sin \phi_0...(ii) From (i) & (ii)sin⁡θ0=2sin⁡(θ0/2)⇒cos⁡(θ02)=1θ02=0⇒θ0=0\begin{aligned} & \sin \theta_0=2 \sin \left(\theta_0 / 2\right) \Rightarrow \cos \left(\frac{\theta_0}{2}\right)=1 \\ & \frac{\theta_0}{2}=0 \\ & \Rightarrow \theta_0=0\end{aligned}(Q) θ0=2ϕ0\textbf{(Q) } \theta_0=2 \phi_0 ...(i) sin⁡θ0=3sin⁡ϕ0\sin \theta_0=\sqrt{3} \sin \phi_0 ...(ii) From (i) & (ii) sin⁡θ0=3sin⁡(θ02)⇒cos⁡(θ02)=32θ02=30,150θ0=60,300 (Rejected) θ0=60,0\begin{aligned} & \sin \theta_0=\sqrt{3} \sin \left(\frac{\theta_0}{2}\right) \\ & \Rightarrow \cos \left(\frac{\theta_0}{2}\right)=\frac{\sqrt{3}}{2} \\ & \frac{\theta_0}{2}=30,150 \\ & \theta_0=60,300 \text{ (Rejected) } \\ & \theta_0=60 , 0\end{aligned}\textbf{(R) } \theta_0=2 \phi_0 sin⁡θ0=3sin⁡ϕ0sin⁡2θ0=3sin⁡ϕ0cos⁡ϕ0=32ϕ0=30,150 (Rejected) \begin{aligned} & \sin \theta_0=\sqrt{3} \sin \phi_0 \\ & \sin 2 \theta_0=\sqrt{3} \sin \phi_0 \\ & \cos \phi_0=\frac{\sqrt{3}}{2} \\ & \phi_0=30,150 \text{ (Rejected) }\end{aligned} \phi_0=30, 0...(iii)...(iii)(S) sin⁡45=2cos⁡ϕ0cos⁡ϕ0=1/2ϕ0=60α=180+2θ0−4ϕ0\begin{aligned} & \textbf {(S) } \sin 45=\sqrt{2} \cos \phi_0 \\ & \cos \phi_0=1 / 2 \\ & \phi_0=60 \\ & \alpha=180+2 \theta_0-4 \phi_0\end{aligned}α=180+90−120\alpha=180+90-120 ...(iv) =180−30;α=150∘=180-30 ; \alpha=150^{\circ}
Practice Ray Optics on Quantrex Academy →

More from Ray Optics

A double convex lens made of glass of refractive index 1.5 and radii of curvature of the… JEE Advanced 2026A beam of polychromatic light passes through a thin prism of prism angle 6^∘ . The… JEE Advanced 2026Consider two isosceles prisms 1 and 2 with prism angles A_1 and A_2 and refractive… JEE Advanced 2026A thin biconvex lens is prepared from the glass ( μ=1.5 ) both curved surfaces of which… JEE Main 2026Light ray incident along a vector AO ( AO = 2 i -3 j ) emerges out along vector OB ( OB =… JEE Main 2026Angle of minimum deviation is equal to the half of the angle of prism in an equilateral… JEE Main 2026A concave mirror of focal length 10 cm forms an image which is double the size of object… JEE Main 2026A spherical interface lens of radius R separates two media of refractive indices 1 and… JEE Main 2026 Full Ray Optics list All JEE Advanced PYQs