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QJEEM20Ph2580: JEE Main 2020 Physics - Class 12 JEEM20Ph2580 Solution: There is a small source of light at some depth below the…

There is a small source of light at some depth below the surface of water (refractive index = 43{4 \over 3} ) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly) :
[Use the fact that surface area of a spherical cap of height h and radius of curvature r is 2 π\pi rh]:

Multiple Choice Options

  • A 17%
  • B 34%
  • C 50%
  • D 21%

Step-by-Step Verified Solution

JEE Main 2020 (Online) 9th January Evening Slot Physics - Geometrical Optics Question 149 English Explanation
43{4 \over 3} sin θ\theta = 1sin90o

sin θ\theta = 34{3 \over 4}

cos θ\theta = 74{{\sqrt 7 } \over 4}

Surface area in solid angle d Ω\Omega = 2 π\pi R2(1 - cos θ\theta )

= 2 π\pi R2(1 - 74{{\sqrt 7 } \over 4} )

Percentage of light = 2πR2(1−74)4πR2{{2\pi {R^2}\left( {1 - {{\sqrt 7 } \over 4}} \right)} \over {4\pi {R^2}}} ×\times 100%

= 4−78{{{4 - \sqrt 7 } \over 8}} ×\times 100%

= 17%

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