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Chapter 35: Q94P (page 1080)

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?

Short Answer

Expert verified

Thus, the difference in the travel times along two routes is 51.6ns.

Step by step solution

01

Light travel along different paths within the central core.

A light ray travelling directly along the central axis reaches the end in time

tdirect=Lv1=n1Lc

For the ray taking the critical zig –zag path, only its velocity component along the core axis direction contributes to reach the other end of the fiber. That component isv1cosθ , so the time of travel for this ray is:

tzig-zag=1v1cosθ=n1Lc1-(sinθn1)2

Using results from the previous solution. Plugging in sinθ=n12-n22and simplifying gives:

tzig-zag=n1Lc(n2n1)=n12Lcn3

02

The difference in the travel times along two routes.

The difference is written as follows:

Δt=tzig-zag-tdirect=n1Lcn3-n1Lc=n1Lcn1n2-1

Withn1=1.58,n2=1.53andL=300 mgives

Δt=n1Lcn1n2-1

=1.58800m3×108m/s1.581.53-1

=5.16×10-8 s

=51.6 ns

Hence, the difference in the travel times along two routes is 51.6ns.

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Most popular questions from this chapter

White light is sent downward onto a horizontal thin film that is sandwiched between two materials. The indexes of refraction are 1.80for the top material, 1.70for the thin film, and 1.50for the bottom material. The film thickness is5×10-7m . Of the visible wavelengths (400 to 700nm ) that result in fully constructive interference at an observer above the film, which is the (a) longer and (b) shorter wavelength? The materials and film are then heated so that the film thickness increases. (c) Does the light resulting in fully constructive interference shift toward longer or shorter wavelengths?

If mirror M2in a Michelson interferometer (fig 35-21) is moved through 0.233mm, a shift of 792 bright fringes occurs. What is the wavelength of the light producing the fringe pattern?

In Fig, monochromatic light of wavelength diffracts through narrow slit S in an otherwise opaque screen. On the other side, a plane mirror is perpendicular to the screen and a distance h from the slit. A viewing screen A is a distance much greater than h. (Because it sits in a plane through the focal point of the lens, screen A is effectively very distant. The lens plays no other role in the experiment and can otherwise be neglected.) Light travels from the slit directly to A interferes with light from the slit that reflects from the mirror to A. The reflection causes a half-wavelength phase shift. (a) Is the fringe that corresponds to a zero path length difference bright or dark? Find expressions (like Eqs. 35-14 and 35-16) that locate (b) the bright fringes and (c) the dark fringes in the interference pattern. (Hint: Consider the image of S produced by the minor as seen from a point on the viewing screen, and then consider Young’s two-slit interference.)

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 ray r3(the light does not reflect inside material 2) and r4(the light reflects twice inside material 2). The waves of and interfere, r3and r4here 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 n3, the type of interference, the thin-layer thickness Lin nanometers, and the wavelength in nanometers of the light as measured in air. Where λis 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.

In Figure 35-50, two isotropic point sources S1and S2emit light in phase at wavelength λand at the same amplitude. The sources are separated by distance d=6.00λon an x axis. A viewing screen is at distance D=20.0λfrom S2and parallel to the y axis. The figure shows two rays reaching point P on the screen, at height yp. (a) At what value of do the rays have the minimum possible phase difference? (b) What multiple of λgives that minimum phase difference? (c) At what value of ypdo the rays have the maximum possible phase difference? What multiple of λgives (d) that maximum phase difference and (e) the phase difference when yp=d? (f) When yp=d, is the resulting intensity at point P maximum, minimum, intermediate but closer to maximum, or intermediate but closer to minimum?
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