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Chapter 35: Q37P (page 1076)

The rhinestones in costume jewellery 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 560nm and of perpendicular incidence will be reflected from the two surfaces of the coating with fully constructive interference?

Short Answer

Expert verified

The minimum thickness of coating with fully constructive interference is 70nm.

Step by step solution

01

Identification of given data

The index of refraction of silicon monoxide layer isnc=2.00

The index of refraction for glass is ng=1.50.

The wavelength of light is 位=560nm.

02

Understanding the concept

The index of refraction is the ratio of the speed of light in medium to speed of light in vacuum

03

Determination of minimum thickness of coating with fully constructive interference

The minimum thickness of coating with fully constructive interference is given as:

t=m+12位2nc

Here, mis order of fringe and its value for minimum thickness for constructive interference is 0.

Substitute all the values in equation.

role="math" localid="1663135130327" t=0+12560nm22=70nm

Therefore, the minimum thickness of coating with fully constructive interference is 70nm.

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