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A coating is being applied to reduce the reflectivity of a pane of glass to light with a wavelength of 522 nm incident near the normal to the pane. If the material has an index of refraction of 1.375, how thick should the coating be?

Answer :

Answer:

  t = 94.91 nm

Explanation:

given,

wavelength of the light = 522 nm

refractive index of the material  = 1.375

we know the equation

       c = ν λ

where ν is the frequency of the wave

           c is the speed of light

   [tex]\nu= \dfrac{c}{\nu\lambda}[/tex]

   [tex]\nu = \dfrac{3\times 10^8}{522 \times 10^{-9}}[/tex]

       ν = 5.75 x 10¹⁴ Hz

the thickness of the coating will be calculated using

        [tex]t = \dfrac{\lambda}{4\mu_{material}}[/tex]

        [tex]t = \dfrac{522 \times 10^{-9}}{4\times 1.375}[/tex]

              t = 94.91 nm

the thickness of the coating will be equal to t = 94.91 nm

The thickness of the coating which is applied to reduce  the reflectivity of a pane of glass to light us 94.91 meter.

How to calculate frequency of the wave?

The frequency of the wave can be calculated using the below formula.

[tex]v=\dfrac{c}{\lambda}[/tex]

Here, [tex]c[/tex] is the speed of light and [tex]\lambda[/tex] is the wavelength of the wave.

Given information-

The wavelength of the light is 522 nm.

Index of refraction of material is 1.375.

As the speed of light is [tex]3\times10^8\rm m/s[/tex]. Thus Put the values in the above formula to find the frequency of the light.

[tex]v=\dfrac{3\times10^8 \rm m/s}{522\times10^{-9}\rm m}\\v=5.75\times10^{14}\rm Hz[/tex]

Hence the frequency of the light is [tex]5.75\times10^{14}\rm Hz[/tex].

The thickness of the coating for the above frequency light wave can be find out using the below formula as,

[tex]t=\dfrac{\lambda}{4\times\mu}[/tex]

Here, [tex]\mu[/tex] is the  index of refraction of material. Thus put the values,

[tex]t=\dfrac{522\times10^{-9}}{4\times1.375}\\t=94.91\rm m[/tex]

Thus the thickness of the coating which is applied to reduce  the reflectivity of a pane of glass to light us 94.91 meter.

Learn more about the frequency of the wave here;

https://brainly.com/question/25699025

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