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Incident Power Transmitted

  1. Jul 16, 2015 #1
    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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    Last edited by a moderator: Jul 16, 2015
  2. jcsd
  3. Jul 17, 2015 #2

    BvU

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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: ).
     
  4. Jul 17, 2015 #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.
     
  5. Jul 17, 2015 #4
    Thank you. I overlooked that fact as well.
     
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