The rhinestones in costume jewelry are glass with index of refraction 1.50. To make them more reflective, they are often coated with a layer of silicon monoxide of index of refraction 2.00. What is the minimum coating thickness needed to ensure that light of wavelength 480 nm and of perpendicular incidence will be reflected from the two surfaces of the coating with fully constructive interference?

The minimum coating thickness needed to ensure that light of wavelength 480 nm and of perpendicular incidence will be reflected from the two surfaces of the coating with fully constructive interference is 60.

Given that, the index of refraction of glass is 1.50 and the index of refraction of silicon monoxide is 2.00. The wavelength light of 480 nm.

If is the wavelength in the coating and λ is the wavelength in vacuum, then    where n is the index of refraction of the coating.

Thus, the minimum coating thickness can be calculated as,

.

For the constructive interference, m = 0.

So

The minimum coating thickness needed to ensure that light of wavelength 480 nm and of perpendicular incidence will be reflected from the two surfaces of the coating with fully constructive interference is 60.

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60

Explanation:

According to the given question, the computation of minimum coating thickness is shown below:-

The condition for constructive interference is

Now we will put the values to the above formula to reach the answer

= 60

Therefore we simply applied the above formula to determine the minimum coating thickness

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explanation:

1= 26.17

2= 1.17

3=30.86

4=5.86

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