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Chapter 33: Q45P (page 1004)

When the rectangular metal tank in the Figure is filled to the top with an unknown liquid, the observer O, with eyes level with the top of the tank, can just see the corner. A ray that refracts towardOthe top surface of the liquid is shown. IfD=85.0cmsoL=1.10m, what is the index of refraction of the liquid?

Figure:

Short Answer

Expert verified

The refractive index of the liquid isn1=1.26.

Step by step solution

01

Given

Consider the given parameters shown below:

L=1.10mD=85cm=0.85mθ2=90°

  1. The Refractive index of vacuum is n2=1.
02

Determine the concept

Use the formula of Snell’s law, which gives the relation between the angle of reflection and the angle of refraction. Before that, the angle of incidence using the equation of tangent ratio can be calculated

03

Determine the refractive index of liquid

Expression for an angle of incidence is as follows:

tanθ1=LDtanθ1=1.100.85θ1=52.31°

Now use Snell’s law:

n1sinθ1=n2sinθ2n1sin52.31=1sin90n1=1.26

So the refractive index of the liquid isn1=1.26 .

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Most popular questions from this chapter

In Fig. 33-66, unpolarized light with an intensity of 25W/m2is sent into a system of four polarizing sheets with polarizing directions at angleslocalid="1662978686975" θ1=40°,θ2=20°,θ3=20°,andθ4=30°. What is the intensity of the light that emerges from the system?

In Fig. 33-73, a long, straight copper wire (diameter2.50 mm and resistance1.00 Ωper300 m ) carries a uniform current of 25 Ain the positive x direction. For point P on the wire’s surface, calculate the magnitudes of (a) the electricfield,E→(b) the magnetic field , B→and (c) the Poynting vector S→, and (d) determine the direction of S→.

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