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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 b=33.734.

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鈥檚 law of refraction, show that the index of refraction of the glass prism is:

n=sin12(+f)sin12f

Formula:

n1蝉颈苍胃1=n2蝉颈苍胃2

03

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

Snell鈥檚 law of refraction gives that

n1蝉颈苍胃1=n2蝉颈苍胃2nb蝉颈苍胃a=na蝉颈苍胃a蝉颈苍胃b=nanb蝉颈苍胃a蝉颈苍胃b=11.8sin90

Substitute the values and solve as:

蝉颈苍胃b=0.55b=33.734

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Most popular questions from this chapter

Question: In Fig. 33-62, a light ray in air is incident at angle 1on a block of transparent plastic with an index of refraction of. The dimensions indicated are H=2.00cmandW=3.00cm. The light passes through the block to one of its sides and there undergoes reflection (inside the block) and possibly refraction (out into the air). This is the point offirst reflection. The reflected light then passes through the block to another of its sides 鈥 a point ofsecond reflection. If 1=40, on which side is the point of (a) first reflection and (b) second reflection? If there is refraction at the point of (c) first reflection, and (d) second reflection, give the angle of refraction; if not, answer 鈥渘one鈥. If 1=70, on which side is the point of (e) first reflection and (f) second reflection? If there is refraction at the point of (g) first reflection, and (h) second reflection, give the angle of refraction; if not, answer 鈥渘one鈥.

Project Seafarer was an ambitious program to construct an enormous antenna, buried underground on a site about 10000km2in area. Its purpose was to transmit signals to submarines while they were deeply submerged. If the effective wavelength were1.0104Earth radii, what would be the (a) frequency and(b) period of the radiations emitted? Ordinarily, electromagnetic radiations do not penetrate very far into conductors such as seawater, and so normal signals cannot reach the submarines.

When red light in vacuum is incident at the Brewster angle on a certain glass slab, the angle of refraction is32 .What are (a) the index of refraction of the glass and (b) the Brewster angle?

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In Fig. 33-77, an albatross glides at aconstant 15m/shorizontallyabove level ground, moving in a vertical plane that contains the Sun. It glides toward a wallof heighth=2.0m, which it will just barely clear. At that time of day, the angle of the Sun relative to the groundis=30.At what speed does the shadow of the albatross move (a) across the level ground and then (b) up the wall? Suppose that later a hawk happens to glide along the same path, alsoat15m/s.You see that when its shadow reaches the wall, the speed of the shadow noticeably increases. (c) Is the Sun now higher or lower in the sky than when the albatross flew by earlier? (d) If the speed of the hawk鈥檚 shadow on the wallis45m/s,what is the angle u of the Sun just then?

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