Solve Light Transmittance Homework: Index Refraction of n=1.5

[pinkberry]

Homework Statement

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.

Homework 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.

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?

 

[rdl]

I would first clarify with the instructor or textbook if the thickness of the plastic disks is necessary for this calculation. If it is not provided, it is possible that the thickness is not relevant for this specific problem and can be assumed to be negligible.

Assuming the thickness is not necessary, the calculation for the fraction of light transmitted can be simplified to T = 1-R, where R is the reflection coefficient. In this case, R = (1-1.5)^2 / (1+1.5)^2 = 0.04, so the fraction of light transmitted is T = 1-0.04 = 0.96 or 96%.

However, if the thickness is necessary, then the calculation would involve using the thickness and the additional equations provided in the problem, such as the one for calculating the intensity of the transmitted light (Itotal). In this case, I would suggest breaking down the problem into smaller steps, calculating the reflection coefficients for each interface and then using the equations to calculate the transmitted intensity at each interface. Finally, the total transmitted intensity can be calculated by multiplying the individual transmitted intensities.

It is also important to note that the assumption of neglecting interference effects may not be accurate in this case, as the problem involves multiple interfaces and the distances between them are not specified. This could lead to interference effects that may affect the final result. As a scientist, it is important to acknowledge and consider potential sources of error in any calculation or experiment.