Ch 33: The Nature and Propagation of Light

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 33: The Nature and Propagation of Light

Problem 11b

Chapter 33, Problem 11b

As shown in Fig. E33.11, a layer of water covers a slab of material X in a beaker. A ray of light traveling upward follows the path indicated. Using the information on the figure, find the angle the light makes with the normal in the air.

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Identify the refractive indices of the materials involved. From the image, Slab 1 has a refractive index \( n_1 = 1.53 \) and Slab 2 has \( n_2 = 1.47 \). The refractive index of air is approximately \( n_3 = 1.00 \).

Apply Snell's Law at the interface between Slab 1 and Slab 2. Snell's Law states \( n_1 \sin \theta_1 = n_2 \sin \theta_2 \), where \( \theta_1 \) is the angle of incidence in Slab 1 and \( \theta_2 = 42^\circ \) is the angle of refraction in Slab 2.

Solve for \( \theta_1 \) using the equation \( \sin \theta_1 = \frac{n_2}{n_1} \sin \theta_2 \). Substitute the known values: \( \sin \theta_1 = \frac{1.47}{1.53} \sin 42^\circ \).

Apply Snell's Law again at the interface between Slab 2 and air. Use \( n_2 \sin \theta_2 = n_3 \sin \theta_3 \), where \( \theta_3 \) is the angle the light makes with the normal in the air.

Solve for \( \theta_3 \) using the equation \( \sin \theta_3 = \frac{n_2}{n_3} \sin \theta_2 \). Substitute the known values: \( \sin \theta_3 = \frac{1.47}{1.00} \sin 42^\circ \). Calculate \( \theta_3 \) using the inverse sine function.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Snell's Law

Snell's Law describes how light bends when it passes from one medium to another. It is given by n1 * sin(θ1) = n2 * sin(θ2), where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles the light makes with the normal in each medium. This law is crucial for calculating the angle of refraction as light moves through different materials.

Refractive Index

The refractive index of a material, denoted as n, is a measure of how much the speed of light is reduced inside the material compared to its speed in a vacuum. It determines how much light bends when entering or exiting the material. In the given image, the refractive indices are 1.53 for Slab 1 and 1.47 for Slab 2, affecting the light's path.

Angle of Incidence and Refraction

The angle of incidence is the angle between the incoming light ray and the normal to the surface at the point of entry. The angle of refraction is the angle between the refracted ray and the normal. Understanding these angles is essential for applying Snell's Law to find the angle the light makes with the normal in the air, as shown in the image.

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Index of Refraction

Related Practice

Textbook Question

A horizontal, parallel-sided plate of glass having a refractive index of 1.52 is in contact with the surface of water in a tank. A ray coming from above in air makes an angle of incidence of 35.0° with the normal to the top surface of the glass. What angle does the ray refracted into the water make with the normal to the surface?

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Textbook Question

Light of a certain frequency has a wavelength of 526 nm in water. What is the wavelength of this light in benzene?

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Textbook Question

Light enters a solid pipe made of plastic having an index of refraction of 1.60. The light travels parallel to the upper part of the pipe (Fig. E33.15). You want to cut the face AB so that all the light will reflect back into the pipe after it first strikes that face. If the pipe is immersed in water of refractive index 1.33, what is the largest that u can be?

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Textbook Question

Light enters a solid pipe made of plastic having an index of refraction of 1.60. The light travels parallel to the upper part of the pipe (Fig. E33.15). You want to cut the face AB so that all the light will reflect back into the pipe after it first strikes that face. What is the largest that u can be if the pipe is in air?

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Textbook Question

Light traveling in air is incident on the surface of a block of plastic at an angle of 62.7° to the normal and is bent so that it makes a 48.1° angle with the normal in the plastic. Find the speed of light in the plastic.

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Textbook Question

(a) A tank containing methanol has walls 2.50 cm thick made of glass of refractive index 1.550. Light from the outside air strikes the glass at a 41.3° angle with the normal to the glass. Find the angle the light makes with the normal in the methanol. (b) The tank is emptied and refilled with an unknown liquid. If light incident at the same angle as in part (a) enters the liquid in the tank at an angle of 20.2° from the normal, what is the refractive index of the unknown liquid?

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