Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced 2019Paper 1
Exam
JEE Advanced
Year
2019
Paper
Paper 1
Subject
Physics
Chapter
Ray Optics

JEE Advanced 2019 · Paper 1 · Physics · Ray Optics

A planar structure of length L and width W is made of two different...

A planar structure of length LL and width WW is made of two different optical media of refractive indices n1=1.5{n}_{1} = 1.5 and n2=1.44{n}_{2} = 1.44 as shown in figure. If L>>W,L > > W, a ray entering from end ABAB will emerge from end CDCD only if the total internal reflection condition is met inside the structure. For L=9.6m,L = 9.6m, if the incident angle θ\theta is varied, the maximum time taken by a ray to exit the plane CDCD is t×10−9s,t \times {10}^{- 9}s, where tt is ____.
[Speed of light c=3×108m/s]c = 3 \times {10}^{8}m / s ]
A planar structure of length L and width W is made of two different optical media of refractive indices n _ 1 = 1.5 and

Correct answer

0

Step-by-step solution

A planar structure of length L and width W is made of two different optical media of refractive indices n _ 1 = 1.5 and
For maximum time taken by a rat to exit, it must travel maximum distance.
So, for this, it should be incident at minimum possible angle i.e., θC{\theta}_{C} at n1−n2{n}_{1} - {n}_{2} boundary.
Applying Snells' law at n1−n2{n}_{1} - {n}_{2} boundary
⇒1.5sinθC=1.44sin⁡90°⇒ 1.5sin{\theta}_{C} = 1.44\sin 90 °
⇒sinθC=1.441.50=2425⇒ sin{\theta}_{C} = \dfrac{1.44}{1.50} = \dfrac{24}{25}
∴sinθC=xd=2425∴ sin{\theta}_{C} = \dfrac{x}{d} = \dfrac{24}{25}
⇒d=25x24⇒ d = \dfrac{25x}{24}
∴∴ total length travel by light =2525×9.6=10m= \dfrac{25}{25} \times 9.6 = 10m \left(as, {x}_\max = L = 9.6m\right)<br><br >∴ t = \dfrac{S}{\left(\dfrac{C}{{n}_{1}}\right)} = \dfrac{10}{\dfrac{3 \times {10}^{n}}{1.5}}\left(t = \dfrac{\text{distance travelled}}{\text{speed of light in medium}}\right)<br><br >= \dfrac{1}{2} \times {10}^{- 7} = 5 \times {10}^{- 9}seconds<br><br >t = 50ns<br><br >t = 50 \times {10}^{- 9}<br><br >∴ Answer = 50
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