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QJEEAdv19Ph6bb2: JEE Advanced 2019 Physics - Class 12 JEEAdv19Ph6bb2 Solution: A planar structure of length L and width W is made of two…

A planar structure of length L and width W is made of two different optical media of refractive indices n1 = 1.5 and n2 = 1.44 as shown in figure. If L >> W, a ray entering from end AB will emerge from end CD. CD only if the total internal reflection condition is met inside the structure. For L = 9.6 m, if the incident angle θ\theta is varied, the maximum time taken by a ray to exit the plane CD is t ×\times 10-9 s, where, t is ................

[Speed of light, c = 3 ×\times 108 m/s]

JEE Advanced 2019 Paper 1 Offline Physics - Geometrical Optics Question 50 English

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JEE Advanced 2019 Paper 1 Offline Physics - Geometrical Optics Question 50 English Explanation

According to total internal reflection (TIR),

1.5sin⁡θc=1.44sin⁡90∘1.5\sin {\theta _c} = 1.44\sin 90^\circ

sin⁡θc=1.441.50=2425\sin {\theta _c} = {{1.44} \over {1.50}} = {{24} \over {25}}

∴\therefore sin⁡θc=xd=2425⇒d=25x24\sin {\theta _c} = {x \over d} = {{24} \over {25}} \Rightarrow d = {{25x} \over {24}}

∴\therefore Total length travelled by light,

∴\therefore t=S(cn1)=103×1081.5=12×10−7=5×10−8t = {S \over {\left( {{c \over {{n_1}}}} \right)}} = {{10} \over {{{3 \times {{10}^8}} \over {1.5}}}} = {1 \over 2} \times {10^{ - 7}} = 5 \times {10^{ - 8}}

t = 50 ns ⇒\Rightarrow t = 50 ×\times 10-9

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