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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 λ=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+12λ2nc

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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Most popular questions from this chapter

In Fig. 35-37, two isotropic point sources S1 and S2 emit identical light waves in phase at wavelengthλ. The sources lie at separation on an x axis, and a light detector is moved in a circle of large radius around the midpoint between them. It detects 30points of zero intensity, including two on the xaxis, one of them to the left of the sources and the other to the right of the sources. What is the value of dλ?

In Fig. 35-44, a broad beam of light of wavelength 630 nm is incident at 90° on a thin, wedge-shaped film with index of refraction 1.50. Transmission gives 10 bright and 9 dark fringes along the film’s length. What is the left-to-right change in film thickness?

Figure 35-57 shows an optical fiber in which a central platic core of index of refractionn1=1.58-is surrounded by a plastic sheath of index of refractionn2=1.53. Light can travel along different paths within the central core, leading to different travel times through the fiber, resulting in information loss. Consider light that travels directly along the central axis of the fiber and light that is repeatedly reflected at the critical angle along the core-sheath interface, reflecting from side to side as it travels down the central core. If the fiber length is 300 m, what is the difference in the travel times along these two routes?

The figure shows the design of a Texas arcade game, Four laser pistols are pointed toward the center of an array of plastic layers where a clay armadillo is the target. The indexes of refraction of the layers are n1=1.55,n2=1.70,n3=1.45,n4=1.60,n5=1.45,n6=1.61,n7=1.59,n8=1.70and n9=1.60. The layer thicknesses are either 2.00 mm or 4.00 mm, as drawn. What is the travel time through the layers for the laser burst from (a) pistol 1, (b) pistol 2, (c) pistol 3, and (d) pistol 4? (e) If the pistols are fired simultaneously, which laser burst hits the target first?

Two waves of light in air, of wavelength λ=600.0nm, are initially in phase. They then both travel through a layer of plastic as shown in Fig. 35-36, with L1=4.00μm, L2=3.50μm, n1=1.40, n2=1.60and. (a) What multiple of λgives their phase difference after they both have emerged from the layers? (b) If the waves later arrive at some common point with the same amplitude, is their interference fully constructive, fully destructive, intermediate but closer to fully constructive,or intermediate but closer to fully destructive?
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