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A transparent. dielectric coating is applied to glass (εr = 4.μr=1, σ= 0) to eliminate the reflection of red light (wavelength in air of 750 nm).

a. What is the required dielectric constant and minimum thickness of the coating?
b. If violet light (wavelength in air of 420 nm) is shone onto this glass coating (6-0). what percentage of the incident power will be reflected?

User Andrew Duffy
by
2.2k points

2 Answers

21 votes
21 votes

Final answer:

To eliminate the reflection of red light with a wavelength of 750 nm, a dielectric coating with a required dielectric constant of 2 and a minimum thickness of 93.75 nm needs to be applied to the glass. The percentage of reflected power for violet light with a wavelength of 420 nm can be calculated using the phase difference between the reflected and transmitted waves due to the coating.

Step-by-step explanation:

To eliminate the reflection of red light with a wavelength of 750 nm, a dielectric coating needs to be applied to the glass. The required dielectric constant can be found using the formula εr = (n^2)/(μr), where n is the index of refraction and μr is the magnetic permeability. In this case, since μr = 1, the dielectric constant would be εr = (n^2)/1 = n^2. Setting εr to 4, we find that the index of refraction n is √4 = 2. Therefore, the required dielectric constant is 2 and the minimum thickness of the coating can be found using the formula t = (λ)/(4n), where λ is the wavelength in air. Substituting the values, we get t = (750 nm)/(4 x 2) = 93.75 nm.

To calculate the percentage of incident power reflected for violet light with a wavelength of 420 nm, we need to determine the phase difference between the reflected and transmitted waves due to the coating. This can be done using the formula δ = (2πnt)/(λ), where δ is the phase difference, n is the index of refraction, t is the thickness of the coating, and λ is the wavelength in air. Substituting the values, we get δ = (2π x 2 x 93.75 nm)/(420 nm) ≈ 3.35 radians. From this, we can calculate the reflection coefficient using the formula R = (sinδ)^2. Finally, we can find the percentage of reflected power by multiplying R by 100.

User Andrey Taritsyn
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2.9k points
17 votes
17 votes

Answer:

a) Dielectric constant ( λ ) = 750 * 10^-9 m

minimum thickness of coating ( d ) = 187.5 nm

b) 3.6%

Step-by-step explanation:

Given data:

wavelength of red light in air = 750 nm

εr = 4

μr = 1, σ = 0

a) Determine the required dielectric constant and min thickness of coating used

Refractive index of coating ( n ) = √εr * μr = √4*1 = 2

the refractive index of glass( ng) = 1.5 which is < 2

λ = 750 * 10^-9 m

Dielectric constant ( λ ) = 750 * 10^-9 m

To determine the minimum thickness we will apply the formula below

d = m λ/2n ; where m = 1

∴ d = 750 nm / 2 ( 2 )

= 187.5 nm

minimum thickness of coating ( d ) = 187.5 nm

b) Determine the percentage of the incident power that will be reflected

R = [ ( n-1 / n + 1 ) - ( n - ng / ng + n ) ]^2

= [ ( 2 - 1 / 2 + 1 ) - ( 2 - 1.5 / 1.5 + 2 ) ]^2

= 0.03628 = 3.6%

User Jayne
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3.3k points