How Is Incident Power Transmitted When Light Hits Water?

  • Thread starter Thread starter KaseyKC
  • Start date Start date
  • Tags Tags
    Power
AI Thread Summary
When light hits water, the percentage of incident power transmitted can be calculated using the amplitude transmission coefficient. The amplitude transmission coefficient formula indicates that the transmitted power should be around 98% when using the amplitude reflection coefficient and conservation of energy, which aligns with university-provided answers. However, an alternative calculation using the transmission coefficient yielded a lower value of approximately 73%. The discrepancy arises because transmittance is not simply equal to the square of the amplitude transmission coefficient due to differences in light speed and direction in the two media. Understanding this relationship clarifies the calculations and resolves the confusion regarding the transmitted power percentage.
KaseyKC
Messages
6
Reaction score
0
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.
 

Attachments

Last edited by a moderator:
Physics news on Phys.org
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: ).
 
  • Like
Likes KaseyKC
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.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Reflection and Transmission of acoustic waves at a boundary
Replies
5
Views
2K
I EM Power transmitted from one region to another (normal incidence)
Replies
6
Views
1K
Light Bulb and Transmitted Intensity?
Replies
1
Views
2K
Odd constraint problem: Reflected and Transmitted Power of String
Replies
8
Views
2K
Air wedge interference pattern after being filled with water
Replies
5
Views
2K
EM wave reflected or transmitted?
Replies
8
Views
3K
How Much Power Can a Coaxial Cable Transmit Before Breakdown?
Replies
1
Views
2K
Mutilple beam reflection question in Fabry-Perot cavity
Replies
1
Views
2K
Reflectance and Transmittance of Light in Water-Glass Interface
Replies
1
Views
2K
Vertically polarized light from a hene laser passes through a linear
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top