Why Are Good Conductors Opaque to Visible Light Based on Skin Depth?

[zak8000]

Homework Statement

for my assignment given i was told to derive the equation of the skin depth of a good conductor and i derived it as

d=sqrt(2/$\mu\omega\sigma$)

then i was told to calculate d where i was given w=10^15 and sigma=10^7 and this gave me a d of d=1.26E-8 which i guess is a small skin depth and then i was given the question:
From this result, explain why good conductors are opaque to visible light?

i know the skin depth represents the depth of the material the wave has to travel before it reaches 1/e of its original value but i don't know how to answer this question.

Homework Equations

The Attempt at a Solution

 

[Spinnor]

Only a very thin foil of a good conductor is needed to either reflect or absorb all the light. You understand that the intensity of light decreases very quickly inside the good conductor and I assume you know what opaque means %^).

 

[rude man]

I think the last equation is dumb. Poor conductors like Carbon are equally opaque to light. Also, good conductors reflect most of the incident wave. Carbon on the other hand absorbs it. Don't see that skin depth has much to do with anything. Refutations welcome.

 

[Aguss]

Hello! I am studying the same thing! Well, let me do an atempt here...

Firstly, remember that in conductors, the wave number is complex, so k = Re(k) + i Im(k)

The expression for k^2 can be derived from maxwell equations. Then you have to take the sqrt of the compley number.

You found that d=sqrt
That you can express it like d = a/(2*pi)

At the same time, d = 1/Im(k)

Re(k) for good conductors is the same that Im(k). Then, you got the wave number k. With it, you can put it into fresnel equation for conductors, and with the reflexion coefficient you can find the relation between "d" and opaque conductors. Let me know what is the conclution you find.

 

[Aguss]

Hello! I am studying the same thing! Well, let me do an atempt here...

Firstly, remember that in conductors, the wave number is complex, so k = Re(k) + i Im(k)

The expression for k^2 can be derived from maxwell equations. Then you have to take the sqrt of the compley number.

You found that d=sqrt
That you can express it like d = a/(2*pi)

At the same time, d = 1/Im(k)

Re(k) for good conductors is the same that Im(k). Then, you got the wave number k. With it, you can put it into fresnel equation for conductors, and with the reflexion coefficient you can find the relation between "d" and opaque conductors. Let me know what is the conclution you find.