There is a small source of light at some depth below the surface of water (refractive index = 4/3) 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 2πrh]

Engineering

Physics

Total Internal Reflection

Question

There is a small source of light at some depth below the surface of water (refractive index = 4/3) 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 2πrh]

34%

17%

50%

21%

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$sinβ = \frac{3}{4}, cosβ = \frac{\sqrt{7}}{4}$

Solid angle d $Ω$ = 2πR² (1 – cos β)

$Percentage of light = \frac{2 {πR}^{2} (1 - cosβ)}{4 {πR}^{2}} \times 100$

$= \frac{1 - cosβ}{2} \times 100 = (\frac{4 - \sqrt{7}}{8}) \times 100 \approx 17 %$