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Chapter 33: Q65P (page 1006)

Question: Figure depicts a simplistic optical fiber: a plastic core(n1=1.58)is surrounded by a plastic sheath (n2=1.53). A light ray is incident on one end of the fiber at angle.The ray is to undergo total internal reflection at point A, where it encounters the core鈥搒heath boundary. (Thus there is no loss of light through that boundary.) What is the maximum value of 胃that allows total internal reflection at A?

Figure:

Short Answer

Expert verified

The maximum value of 胃that allows total internal reflection at A is 23.2鈭�.

Step by step solution

01

Given

  1. Refractive index of the plastic core,n1=1.58
  2. Refractive index of the plastic sheath,n2=1.53
02

Understanding the concept

By using the concept of the critical angle and Snell鈥檚 law, we can find the value of 胃that allows the total internal reflection.

Formula:

Critical angle is

胃c=sin-1n2n1

Snell鈥檚 law is :

n1蝉颈苍胃1=n2蝉颈苍胃2

03

Calculate the maximum value of θ that allows total internal refection at A.

The critical angle is given by

胃c=sin-1n2n1胃c=sin-11.531.58=75.547鈭�

So, by geometry, the incident angle is

胃1=90-胃c胃1=90-75.547o=14.45鈭�

Now, we have to apply Snell鈥檚 law,

nairsin胃=n1sin胃1

Since nair=1

sin胃=1.58sin14.45鈭�sim胃=0.3942胃=23.2鈭�

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Most popular questions from this chapter

In Fig. 33-51, light is incident at angle 胃1=40.1掳on a boundary between two transparent materials. Some of the light travels down through the next three layers of transparent materials, while some of it reflects upward and then escapes into the air. Ifn1=1.30,鈥�n2=1.40,鈥�n3=1.32andn4=1.45, what is the value of

(a)胃5in the air and

(b) 胃4in the bottom material?

The maximum electric field 10 mfrom an isotropic point source of light is 2.0 V/m. What are (a) the maximum value of the magnetic field and (b) the average intensity of the light there? (c) What is the power of the source?

In Fig.33-52a, a beam of light in material1is incident on a boundary at an angle of胃1=30掳. The extent of refraction of the light into material2depends, in part, on the index of refractionn2of material 2. Fig.33-52bgives the angle of refraction胃2versusn2for a range of possiblen2values. The vertical axis scale is set by胃2a=20.0掳and胃2b=40.0掳

(a) What is the index of refraction of material 1?

(b) If the incident angle is changed to60掳and material 2has n2=2.4, then what is angle 胃2?

A certain helium鈥搉eon laser emits red light in a narrow band of wavelengths centered at632.8nm and with a 鈥渨avelength width鈥� (such as on the scale of Fig. 33-1) of0.0100nm. What is the corresponding 鈥渇requency width鈥� for the emission?

In Fig. 33-78, where n1=1.70, n2=1.50,andn3=1.30,light refracts from material 1 into material 2. If it is incident at point A at the critical angle for the interface between materials 2 and 3, what are (a) the angle of refraction at pointBand (b) the initialangle胃?If, instead, light is incident atBat the critical angle for the interface between materials 2 and 3, what are (c) the angle of refraction at pointAand (d) the initial angle胃? If, instead of all that, light is incident at point Aat Brewster鈥檚 angle for the interface between materials 2 and 3, what are (e) the angle of refraction at point B and (f) the initialangle胃?
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