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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=0.85m胃2=90掳

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

Determine the concept

Use the formula of Snell鈥檚 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:

迟补苍胃1=LDtan胃1=1.100.85胃1=52.31掳

Now use Snell鈥檚 law:

n1蝉颈苍胃1=n2蝉颈苍胃2n1sin52.31=1sin90n1=1.26

So the refractive index of the liquid isn1=1.26 .

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Most popular questions from this chapter

Question: The index of refraction of benzene is1.8. What is the critical angle for a light ray traveling in benzene toward a flat layer of air above the benzene?

In the arrangement of Fig. 33-15a, start with light that is initially polarized parallel to the x axis, and write the ratio of its final intensity I3to its initial intensity I0 asrole="math" localid="1662979786202" I3/I0=Acosn胃 . What are A, n, and 胃if we rotate the polarizing direction of the first sheet (a)60掳 counterclockwise and (b)90掳 clockwise from what is shown?

Question: In the Figure, light enters a 90鈭�triangular prism at point Pwith incident angle 胃, and then some of it refracts at point Qwith an angle of refraction of 90鈭�.(a) What is the index of refraction of the prism in terms of 胃?(b) What, numerically, is the maximum value that the index of refraction can have?(c) Does light emerge at Qif the incident angle at Pis increased slightly? and (d) Does light emerge at Qif the incident angle at Pis decreased slightly?

Figure:

In the figure, a ray is incident on one face of a triangular glass prism in air. The angle of incidence 胃is chosen so that the emerging ray also makes the same angle 胃with the normal to the other face. Show that the index ofrefraction of the glass prism is given by

蠄n=sin12(蠄+蠒)sin12蠒

where蠒 is the vertex angle of the prism and 蠄is thedeviation angle, the total angle through which the beam is turned in passing through the prism. (Under these conditions the deviation angle has the smallest possible value, which is called theangle of minimum deviation.)

Figure:

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