How Is Incident Power Transmitted When Light Hits Water?

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SUMMARY

The discussion focuses on the transmission of incident light power when it strikes water, specifically with a refractive index of 1.334. The amplitude transmission coefficient (t) and amplitude reflection coefficient (r) are critical in calculating the transmitted power, with the correct answer being 98% based on the conservation of energy. A common misconception is that the transmittance T equals |t|²; however, due to the differing speed of light in air and water, this is not the case. The correct approach involves recognizing that transmission and reflection coefficients must sum to one.

PREREQUISITES
  • Understanding of refractive indices, specifically for water (n = 1.334).
  • Familiarity with amplitude transmission (t) and reflection (r) coefficients.
  • Knowledge of conservation of energy principles in optics.
  • Basic grasp of light behavior at media interfaces.
NEXT STEPS
  • Study the derivation and application of the amplitude transmission coefficient in optics.
  • Learn about the implications of Snell's Law on light transmission and reflection.
  • Investigate the relationship between speed of light in different media and its effect on transmittance.
  • Explore practical applications of these concepts in optical engineering and photonics.
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Students and professionals in physics, optical engineering, and anyone interested in understanding light behavior at the interface of different media, particularly in applications involving water and air.

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1. Light is incident normally from air onto the surface of water whose refractive index is 1.334 2 nH O = . Assuming zero absorption of the light what is the percentage of incident power that is transmitted into the water?2. Amplitude transmission coefficient (t=2ns/ns+nu) and Amplitude reflection coefficient (r=ns-nu/ns+nu)3. Refer to Page 3 biii) in the included PDF for the supposed correct answer as given by my university. It chooses to use the amplitude reflection coefficient and then the conservation of energy to get an answer of 98%. I got this answer as well using this method. However it seemed more intuitive to me to use the transmission coefficient instead as we want the power TRANSMITTED so I proceeded to plug in the numbers into the equation I've given above. I however got an answer close to 73%. Could someone help me in where I went wrong.
 

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Hello again,

found your expression for t here. There it also says:

The transmittance T is generally not equal to |t|2, since the light travels with different direction and speed in the two media. The transmittance is related to t by:[6]​
09742eb559702863eee18d7d043e8dfd.png

and that solves your mystery: the perpendicular direction makes the cosines 1, so the speed is the culprit. Not unlogical, but easy to overlook (as I did too :smile: ).
 
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Transmission + Reflection coefficients should add to be one.

This is true not only with the numberical results, but also with the formulas that are used to compute them (before plugging in numbers).

Sort this out and you will see the error.
 
BvU said:
Hello again,

found your expression for t here. There it also says:

The transmittance T is generally not equal to |t|2, since the light travels with different direction and speed in the two media. The transmittance is related to t by:[6]​
09742eb559702863eee18d7d043e8dfd.png

and that solves your mystery: the perpendicular direction makes the cosines 1, so the speed is the culprit. Not unlogical, but easy to overlook (as I did too :smile: ).

Thank you. I overlooked that fact as well.
 

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