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 12a

Chapter 33, Problem 12a

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?

Verified step by step guidance

Identify the mediums involved: air, glass, and water. The refractive indices are n_air = 1.00, n_glass = 1.52, and n_water = 1.33.

Apply Snell's Law at the air-glass interface. Snell's Law is given by:

n_{1} \sin θ = n_{2} \sin θ

. Here, n1 = 1.00 (air), θ1 = 35.0°, and n2 = 1.52 (glass). Solve for the angle of refraction θ2 in the glass.

Calculate the angle of refraction in the glass using the formula:

\sin θ = \frac{n_{1} \sin θ}{n_{2}}

. Substitute the known values to find θ2.

Apply Snell's Law again at the glass-water interface. Use n_glass = 1.52 and n_water = 1.33. The angle of incidence at this interface is the angle of refraction from the previous step.

Solve for the angle of refraction in the water using Snell's Law:

n_{2} \sin θ = n_{3} \sin θ

. Substitute the values to find the angle of refraction in the water.

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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 the equation 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 of incidence and refraction, respectively. This law is crucial for calculating the angle of refraction when light enters a different medium.

Refractive Index

The refractive index of a medium quantifies how much light slows down and bends when entering the medium. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium. A higher refractive index indicates greater bending of light. In this problem, the refractive indices of air, glass, and water are essential for applying Snell's Law.

Angle of Incidence and Refraction

The angle of incidence is the angle between the incoming 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 crucial for applying Snell's Law to determine how the ray bends as it passes through different media, such as from air to glass and then to water.

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Index of Refraction

Related Practice

Textbook Question

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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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

The critical angle for total internal reflection at a liquid–air interface is 42.5°. If a ray of light traveling in the liquid has an angle of incidence at the interface of 35.0°, what angle does the refracted ray in the air make with the normal?

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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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