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Chapter 33: Q58P (page 1005)

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?

Short Answer

Expert verified

The critical angle for the light ray is θb=33.7∘≈34∘.

Step by step solution

01

Given

The refractive index is nb=1.8.

02

Determine the concept for the Snell’s law as:

Write for the angle of refraction in terms of the vertex angle from the geometry of the prism and the ray diagram. Then using the formula for the exterior angle of triangle, solve for the angle of incidence in terms of the vertex angle. Then, using Snell’s law of refraction, show that the index of refraction of the glass prism is:

n=sin12(ψ+f)sin12f

Formula:

n1sinθ1=n2sinθ2

03

Calculate the critical angle for a light ray traveling in benzene toward a flat layer of air above the benzene

Snell’s law of refraction gives that

n1sinθ1=n2sinθ2nbsinθa=nasinθasinθb=nanbsinθasinθb=11.8sin90∘

Substitute the values and solve as:

sinθb=0.55θb=33.7∘≈34∘

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Most popular questions from this chapter

Question: Suppose the prism of Fig. 33-53 has apex angle ϕ=60oand index of refractionn=1.60 . (a) What is the smallest angle of incidenceθ for which a ray can enter the left face of the prism and exit the right face? (b) What angle of incidenceθ is required for the ray to exit the prism with an identical angleθ for its refraction, as it does in Fig. 33-53?

Figure:

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:

In Figure

(a), a beam of light in a material1is incident on a boundary at an angle θ1=40°. Some of the light travels through the material 2, and then some of it emerges into the material 3. The two boundaries between the three materials are parallel. The final direction of the beam depends, in part, on the index of refraction n3of the third material. Figure (b) gives the angle of refraction θ3in that material versus n3a range of possiblen3values. The vertical axis scale is set byθ3a=30.0° and θ3b=50.0°.(a) What is the indexof refraction of material , or is the index impossible to calculate without more information?

(b) What is the index of refraction of material 2, or is the index impossible to calculate without more information?

(c) It θ1is changed to 70°and the index of refraction of a material 3 is2.4 , what is θ3?

Figure:

Light in a vacuum is incident on the surface of a glass slab. In the vacuum, the beam makes an angle of32.0°with the normal to the surface, while in the glass it makes an angle of21.0°with the normal. What is the index of refraction of the glass?

In a region of space where gravitational forces can be neglected, a sphere is accelerated by a uniform light beam ofintensity6.0 mW/m2.The sphere is totally absorbing and has a radius of2.0 μmand a uniform density of5.0×103 kg/m3. What is the magnitude of the sphere’s acceleration due to the light?
See all solutions

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