A plane electromagnetic wave in “medium 1†is given as: E 1 = E 01 Sin[(3 π

Question

A plane electromagnetic wave in “medium 1†is given as:

E1 = E01Sin[(3Ï€)z-(8Ï€ x 108)t] <?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

And as E2= E02Sin[(4Ï€)z-(8Ï€ x 108)t] in “medium 2â€.

What is the index of refraction for “medium 1�

What is the index of refraction for “medium 2�

Can you achieve total internal reflection for this EM wave going from “medium 1 to 2†or from “medium 2 to 1â€. Explain your reasoning.

Use Snell’s law to find the critical angle where the total internal reflection occurs?

Explanation / Answer

1.

V1 = (8*10^8)/3 = 2.66667 *10^8 m/s

V2 = (8*10^8 )/4 = 2 *10^8 m/s

n1 = 3/(8/3) = 9/8 = 1.125

n2 = 3/2 = 1.5

TIR occurs when the first medium has a larger refractive index than the second medium ,

hence TIR will occur when light travels from 2 to 1.

[c]

critical angle = sin^-1(n2/n1),

here in this case for TIR to occur ,they are switched

theta = sin^-1(1.125/1.5)

theta = 48.5903.

critical angle = 48.5903

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