How Is Incident Power Transmitted When Light Hits Water?

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Homework Help Overview

The discussion revolves around the transmission of incident light power when it strikes the surface of water, specifically focusing on the calculations involving the amplitude transmission and reflection coefficients. The original poster presents a scenario involving light transitioning from air to water, with a refractive index of 1.334, and seeks clarification on the discrepancy between their calculated transmission percentage and that provided by their university.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to use both the amplitude transmission coefficient and the amplitude reflection coefficient to calculate the percentage of transmitted power, questioning where their calculations may have diverged from expected results. Other participants discuss the relationship between transmittance and the coefficients, noting the impact of light speed in different media.

Discussion Status

Participants are actively engaging with the problem, with some providing insights into the relationships between coefficients and the effects of light traveling through different media. There is a recognition of the complexities involved in the calculations, and guidance has been offered regarding the assumptions made in the original poster's approach.

Contextual Notes

The discussion includes references to specific formulas for calculating transmission and reflection coefficients, as well as a mention of a PDF provided by the original poster that contains additional context. There is an acknowledgment of potential oversight regarding the effects of light speed and direction in the two media.

KaseyKC
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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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