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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

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.)

Someone plans to float a small, totally absorbing sphere 0.500m above an isotropic point source of light so that the upward radiation force from the light matches the downward gravitational force on the sphere. The sphere鈥檚 density is 19.0 g/cm3, and its radius is 2.00mm. (a) What power would be required of the light source? (b) Even if such a source were made, why would the support of the sphere be unstable?

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?

The magnetic component of a polarized wave of light is given by.Bx=(4渭T)sin[ky+(2脳1015s-1)t (a) In which direction does the wave travel, (b) parallel to which axis is it polarized, and (c) what is its intensity? (d) Write an expression for the electric field of the wave, including a value for the angular wave number. (e) What is the wavelength? (f) In which region of the electromagnetic spectrum is this electromagnetic wave?

In Fig. 33-73, a long, straight copper wire (diameter2.50鈥尘尘 and resistance1.00鈥坝﹑别谤300鈥尘 ) carries a uniform current of 25鈥碱in the positive x direction. For point P on the wire鈥檚 surface, calculate the magnitudes of (a) the electricfield,E鈫�(b) the magnetic field , B鈫�and (c) the Poynting vector S鈫�, and (d) determine the direction of S鈫�.
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