How Is Incident Power Transmitted When Light Hits Water?

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In summary, the conversation discusses the percentage of incident power that is transmitted into water when light is incident normally from air. The refractive index of water is given as 1.334 and there is assumed to be no absorption of light. The conversation also mentions the amplitude transmission and reflection coefficients, and how they should add up to one. There is a discrepancy in the final answer obtained using the transmission coefficient and the one obtained using the reflection coefficient. It is later discovered that this is due to the difference in direction and speed of light in the two media.
  • #1
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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  • #2
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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  • #3
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.
 
  • #4
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.
 

Related to How Is Incident Power Transmitted When Light Hits Water?

1. What is incident power transmitted?

Incident power transmitted refers to the amount of power that is successfully transferred from one medium to another without being reflected or absorbed. It is an important concept in optics and other fields where energy transfer is involved.

2. How is incident power transmitted calculated?

The incident power transmitted is calculated by taking the ratio of the transmitted power to the incident power. This can be expressed as a decimal or a percentage. For example, if 80% of the incident power is transmitted, the incident power transmitted would be 0.8 or 80%.

3. What factors affect the incident power transmitted?

The incident power transmitted can be affected by various factors, such as the angle of incidence, the refractive index of the mediums, and the surface characteristics of the mediums. In general, a higher angle of incidence and a lower refractive index will result in a lower incident power transmitted.

4. Why is incident power transmitted important?

Incident power transmitted is important because it determines the efficiency of energy transfer between mediums. It is used in various applications, such as in optical instruments, telecommunications, and medical imaging. Understanding and controlling incident power transmitted is crucial for achieving desired results in these fields.

5. How can incident power transmitted be optimized?

To optimize incident power transmitted, one can use techniques such as anti-reflection coatings, which reduce the amount of reflected energy, and adjusting the angle of incidence to minimize the amount of energy absorbed. Additionally, using mediums with a similar refractive index can also help to increase the incident power transmitted.

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