Question

Jee advance previous year question
________________________A solid glass cube ,edge length 10mm ,refractive index 1.50 has a small air bubble at it's centre . what minimum fraction of cubes' surface must be covered to prevent the bubble from being seen , no matter what be the direction of viewing?​

Answer 1

Answer:

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Answer 2

• Solution:-

Let L = length of edge of cube . light leaving the bubble at angle ¢ is totally reflected . when ¢ = ¢ᶜ

so, sach face of cube must be covered (to prevent bubble from being visible ) is a Circle of radius r that is associated with the angle ¢ᶜ

Now , sin¢ᶜ = 1/n

and , r = L/2tan¢ᶜ = L/2×1/√n²-1)

r = 10 /2√(1.5)²-1 => 4.47mm

There 6 faces of cube ,so six discs of radius r are required . fraction of surface area that must be covered is

f = 6πr²/6L² = πr²/L²= π(4.47)²/10² = 0.63 Answer

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