Essential University Physics
4th Edition
ISBN: 9780134988566
Author: Wolfson, Richard
Publisher: Pearson Education,
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Chapter 30, Problem 59P
To determine
Show that
ϕ = 4 sin − 1 ( sin θ n ) − 2 θ
.
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Light, when incident on a given surface, presents a reflected and a refracted component. When the reflected beam is perpendicular to the refracted beam, the angle of incidence θᵢ is called Brewster's angle. If a beam of light is initially in air with index of refraction n₁ = 1 and is incident on a glass surface (index of refraction n₂ = 1.5), Brewster's angle is:
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θ1 = 51.1
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Chapter 30 Solutions
Essential University Physics
Ch. 30.1 - Prob. 30.1GICh. 30.2 - The figure shows the path of a light ray through...Ch. 30.3 - The glass prism in Fig. 30.11 has n = 1.5 and is...Ch. 30.4 - Prob. 30.4GICh. 30 - Prob. 1FTDCh. 30 - Why does a spoon appear bent when its in a glass...Ch. 30 - Prob. 3FTDCh. 30 - Prob. 4FTDCh. 30 - You send white light through two identical glass...Ch. 30 - In glass, which end of the visible spectrum has...
Ch. 30 - Prob. 7FTDCh. 30 - Why are polarizing sunglasses better than glasses...Ch. 30 - Under what conditions will the polarizing angle be...Ch. 30 - Through what angle should you rotate a mirror so...Ch. 30 - Prob. 12ECh. 30 - To what angular accuracy must two ostensibly...Ch. 30 - Prob. 14ECh. 30 - In which substance in Table 30.1 does the speed of...Ch. 30 - Information in a compact disc is stored in pits"...Ch. 30 - Light is incident on an air-glass interface, and...Ch. 30 - A light ray propagates in a transparent material...Ch. 30 - Light propagating in the glass (n = 1.52) wall of...Ch. 30 - Prob. 20ECh. 30 - Find the refractive index of a material for which...Ch. 30 - Find the critical angle for total internal...Ch. 30 - A drop of water is trapped in a block of ice....Ch. 30 - What is the critical angle for light propagating...Ch. 30 - Total internal reflection occurs at an interface...Ch. 30 - Blue and red laser beams strike an air-glass...Ch. 30 - White light propagating in air is incident at 45...Ch. 30 - Example 30.2: Take the slab in Fig 30.6 to be...Ch. 30 - Example 30.2: Take θ1 = 32.5° in Fig 30.6. (a) If...Ch. 30 - Prob. 30ECh. 30 - Prob. 31ECh. 30 - Prob. 32ECh. 30 - Prob. 33ECh. 30 - Prob. 34ECh. 30 - Prob. 35ECh. 30 - Suppose the 60 angle in Fig. 30.18 is changed to...Ch. 30 - The refractive index of a human cornea is 1.40. If...Ch. 30 - Two plane mirrors make an angle . A light ray...Ch. 30 - An unlabeled bottle of liquid has spilled, and...Ch. 30 - A meter stick lies on the bottom of the...Ch. 30 - Prob. 41PCh. 30 - At the aquarium where you work, a fish has gone...Ch. 30 - Prob. 43PCh. 30 - You've dropped your car keys at night off the end...Ch. 30 - Laser eye surgery uses ultraviolet light with...Ch. 30 - Prob. 46PCh. 30 - Where and in what direction would the main beam...Ch. 30 - Find the speed of light in a material for which...Ch. 30 - Prob. 49PCh. 30 - For the interface between air (refractive index 1)...Ch. 30 - A scuba diver sets off a camera flash at depth h...Ch. 30 - Suppose the red and blue beams of Exercise 26 are...Ch. 30 - In cataract surgery, ophthalmologists replace the...Ch. 30 - In a ruby laser, light is produced in a solid rod...Ch. 30 - An optical fiber with circular cross section has...Ch. 30 - A cylindrical tank 2.4 m deep is full to the brim...Ch. 30 - For what diameter tank in Problem 50 will sunlight...Ch. 30 - Prob. 58PCh. 30 - Prob. 59PCh. 30 - (a) Differentiate the result of Problem 55 to show...Ch. 30 - Prob. 61PCh. 30 - Show that a three-dimensional corner reflector...Ch. 30 - Fermat's principle states that a light ray's path...Ch. 30 - Prob. 64PCh. 30 - A slab of transparent material has thickness d and...Ch. 30 - For common materials like glass, the wavelength...Ch. 30 - Figure 30.25a depicts lights path over a hot road,...Ch. 30 - Prob. 68PPCh. 30 - Figure 30.25b shows how continuous refraction in...Ch. 30 - The refractive index in the ionosphere is strongly...
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- A light beam is traveling through an unknown substance. When it strikes a boundary between that substance and the air (?air≈1),(nair≈1), the angle of reflection is 25.0∘25.0∘ and the angle of refraction is 47.0∘.47.0∘. What is the index of refraction ?n of the substance?arrow_forwardLight traveling in a medium of index of refraction n1 is incident on another medium having an index of refraction n2. Under which of the following conditions can total internal reflection occur at the interface of the two media? (a) The indices of refraction have the relation n2 n1. (b) The indices of refraction have the relation n1 n2. (c) Light travels slower in the second medium than in the first. (d) The angle of incidence is less than the critical angle. (e) The angle of incidence must equal the angle of refraction.arrow_forwardA goldfish is swimming inside a spherical bowl of water having an index of refraction n = 1.333. Suppose the goldfish is p = 10.0 cm from the wall of a howl of radius |R| = 15.0 cm. as in Figure P23.22. Neglecting the refraction of light caused by the wall of the bowl, determine the apparent distance of the goldfish from the wall according to an observer outside the bowl. Figure P23.22arrow_forward
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