Light Transmittance

[pinkberry]

1. The problem statement, all variables and given/known data
Light of wavelength 5000 angstroms is incident normally on a series of two transparent plastic disks separated by a distance large compared with the wavelength. If the index o refraction of the disks is n=1.5, what fraction of the light is transmitted? Neglect absorption, internal multiple reflections, and interference effects.


2. Relevant equations
T = 1+R
R = (n1-n2)/(n1+n2), where n is the index of refraction depending on the material

Itotal is proportional to |Etotal|^2 = Etot * (Etot*) where (Etot*) is the complex conjugate.



3. The attempt at a solution
R = (1-1.5)/(1+1.5) = -0.20: going from air to the disk1
Similar calculations for air to disk1, disk1 to air, air to disk2, and disk2 to air.

I tried to calculate Etotal as:
Etotal = -0.20*E0 + 0.20E0* e^(i*delta)
delta = 2kd = 2*(2pi/lambda)*d where d = thickness of the disc
but I am not given a thickness...

Am I missing an equation I need to use? Approaching this from the wrong angle?
Any advice would help! Thank you.

[Lambduh]

You've got an error in your equation for reflectivity. It should be ((n1 - n2)/(n1 +n2))^2

which gives me an r = 0.04 or 4%. So that means 96% of light incident on each plate will transmit through... work from there:)

Also for this thickness won't matter too much but remember that there is an interface at the front and the back of the plate... so really you've got 4 interfaces to find the transmission through.

[pinkberry]

Thanks lambduh! I think I figured it out. :)

[Ravian]

is not it R+T=1 giving T=1-R?