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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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Most popular questions from this chapter

Transmission through thin layers. In Fig. 35-43, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) Part of the light ends up in material 3 as rayr3(the light does not reflect inside material 2) andr4(the light reflects twice inside material 2). The waves ofr3and r4interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). For this situation, each problem in Table 35-3 refers to the indexes of refraction n1,n2and n3the type of interference, the thin-layer thickness Lin nanometers, and the wavelength 位in nanometers of the light as measured in air. Where位is missing, give the wavelength that is in the visible range. Where Lis missing, give the second least thickness or the third least thickness as indicated.

The reflection of perpendicularly incident white light by a soap film in the air has an interference maximum at 600nmand a minimum at role="math" localid="1663024492960" 450nm, with no minimum in between. If n=1.33for the film, what is the film thickness, assumed uniform?

Three electromagnetic waves travel through a certain point P along an x-axis. They are polarized parallel to a y-axis, with the following variations in their amplitudes. Find their resultant at P.

E1=(10.00渭痴/m)sin[2脳1014t]E2=(5.00渭痴/m)sin[2脳1014t+45掳]E3=(5.00渭痴/m)sin[2脳1014t-45掳]

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?
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