Ch 33: The Nature and Propagation of Light

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

Young & Freedman Calc 15th Edition

Ch 33: The Nature and Propagation of Light

Problem 6

Chapter 32, Problem 6

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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Identify the relationship between the speed of light, frequency, and wavelength in a medium. The speed of light in a medium is given by the equation:

v = f λ

, where

v

is the speed of light in the medium,

f

is the frequency, and

λ

is the wavelength.

Understand that the frequency of light remains constant when it travels from one medium to another. Therefore, the frequency of light in water is the same as in benzene.

Use the refractive index to relate the speed of light in different media. The refractive index

n

of a medium is defined as

n = \frac{c}{v}

, where

c

is the speed of light in vacuum and

v

is the speed of light in the medium.

Calculate the speed of light in water using its refractive index. For water, the refractive index is approximately 1.33. Thus,

v

_water = c1.33.

Calculate the wavelength of light in benzene using its refractive index. For benzene, the refractive index is approximately 1.50. Use the relationship

λ

_benzene = λ_watern_water n_benzene to find the wavelength in benzene.

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Key Concepts

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

Refraction and Refractive Index

Refraction is the bending of light as it passes from one medium to another, due to a change in its speed. The refractive index is a measure of how much the speed of light is reduced inside a medium compared to vacuum. It is crucial for determining how light's wavelength changes when moving between different substances.

Wavelength and Frequency Relationship

The wavelength of light is inversely proportional to its frequency, given by the equation c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency. In different media, while the speed and wavelength change, the frequency remains constant, which is key to finding the new wavelength in benzene.

Speed of Light in Different Media

The speed of light varies in different media, being slower in denser materials. This speed is calculated using v = c/n, where v is the speed of light in the medium, c is the speed of light in vacuum, and n is the refractive index. Understanding this helps in determining how the wavelength changes as light enters benzene from water.

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Related Practice

Textbook Question

A beam of light has a wavelength of 650 nm in vacuum. What is the wavelength of these waves in the liquid?

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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

Two plane mirrors intersect at right angles. A laser beam strikes the first of them at a point 11.5 cm from their point of intersection, as shown in Fig. E33.1. For what angle of incidence at the first mirror will this ray strike the midpoint of the second mirror (which is 28.0 cm long) after reflecting from the first mirror?

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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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