A point source of power $$4W$$ is placed $$1m$$ below the free surface of liquid whose refractive index is '$$23$$ ’. Find the rate of transfer of energy (in$$ $$watt) from the liquid surface to air. Ignore any absorption or scattering of light energy.

Question

A point source of power $$4W$$ is placed $$1m$$ below the free surface of liquid whose refractive index is '$$23$$ ’. Find the rate of transfer of energy (in$$ $$watt) from the liquid surface to air. Ignore any absorption or scattering of light energy.

Infinity Learn · Accepted Answer

The light escape is confined within a cone of apex angle '2 $θ_{c}$ ' where c $θ_{c}$ is the critical angle. Imagine a sphere with source of light as its centre and the surface area abc is A.
$A = \int_{0}^{θ_{c}} 2 {πR}^{2} \sin θdθ = 2 {πR}^{2} (1 - \cos θ_{c})$
$= {πR}^{2} [∴ θ_{c} = \sin^{- 1} (\frac{\sqrt{3}}{2}) = 60^{\circ}]$
$∴ Power transfer = P \times \frac{A}{4 {πR}^{2}} = 4 \times \frac{1}{4} = 1 W$

Total internal reflection - Ray optics and optical instruments

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A point source of power 4W is placed 1m below the free surface of liquid whose refractive index is ' $\frac{2}{\sqrt{3}}$ ’. Find the rate of transfer of energy (in watt) from the liquid surface to air. Ignore any absorption or scattering of light energy.

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Total internal reflection - Ray optics and optical instruments

Remember concepts with our Masterclasses.

A point source of power 4W is placed 1m below the free surface of liquid whose refractive index is '23 ’. Find the rate of transfer of energy (in watt) from the liquid surface to air. Ignore any absorption or scattering of light energy.

The light escape is confined within a cone of apex angle '2θc ' where c θc is the critical angle. Imagine a sphere with source of light as its centre and the surface area abc is A.A=∫0θc 2πR2sin⁡θdθ=2πR21−cos⁡θc=πR2 ∴θc=sin−1⁡32=60∘∴ Power transfer =P×A4πR2=4×14=1W

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A point source of power 4W is placed 1m below the free surface of liquid whose refractive index is ' $\frac{2}{\sqrt{3}}$ ’. Find the rate of transfer of energy (in watt) from the liquid surface to air. Ignore any absorption or scattering of light energy.