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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. 33-40, initially unpolarized light is sent into a system of three polarizing sheets whose polarizing directions make angles of 胃1=40掳, 胃2=20掳, and胃2=40掳with the direction of theyaxis. What percentage of the light鈥檚 initial intensity is transmitted by the system? (Hint: Be careful with the angles.)

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?

Assume (unrealistically) that a TV station acts as a point source broadcasting isotopically at 1.0鈥�MW. What is the intensity of the transmitted signal reaching Proxima Centauri, the star nearest our solar system,4.3鈥�lyaway? (An alien civilization at that distance might be able to watchXFiles.) A light-year (ly) is the distance light travels in one year.

From Fig.33-2, approximate the (a) smaller (b) larger wavelength at which the eye of a standard observer has half the eye鈥檚 maximum sensitivity. What are the (c) wavelength, (d) frequency, and (e) period of the light at which the eye is the most sensitive?

Figure 33-30 shows rays of monochromatic light propagating through three materials a, b, and c. Rank the materials according to the index of refraction, greatest first.
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