Book cover for University Physics with Modern Physics

University Physics with Modern Physics

Hugh D. Young, Roger A. Freeman

ISBN #9780321501219

12th Edition

3,769 Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter section explores the essential properties and propagation behaviors of light, including reflection, refraction, dispersion, polarization, and scattering. It discusses the different models of light and highlights Huygens's principle as a framework for understanding wave propagation. The content connects these concepts to natural phenomena and technological applications, reinforcing the foundational role of light in both the natural world and modern optics.

Learning Objectives

1

Understand the fundamental properties of light including reflection, refraction, dispersion, polarization, and scattering.

2

Analyze and compare different models of light (particle, ray, and wave) and their applications.

3

Explain Huygens's principle and its role in connecting various behaviors of light.

4

Apply optical principles to explain natural phenomena such as the blue sky and rainbows.

5

Relate the basic properties of light to advanced technological applications in optics.

Key Concepts

CONCEPT

DEFINITION

Reflection

The process by which light bounces off a surface, following the law that the angle of incidence equals the angle of reflection.

Refraction

The bending of light as it passes from one medium to another due to a change in its speed, described by Snell's law.

Dispersion

The separation of light into its component wavelengths (colors) as it passes through a medium, such as a prism.

Polarization

The orientation of the oscillations of the electromagnetic waves of light in a particular direction.

Scattering

The redirection of light in many directions due to interactions with particles or irregularities in a medium.

Particle Model

A model of light that considers light as composed of particles called photons.

Ray Model

A simplified model where light travels in straight lines called rays, useful in geometrical optics.

Wave Model

A model that describes light as electromagnetic waves with varying amplitudes and frequencies.

Huygens's Principle

A principle that states every point on a wavefront can be considered a source of secondary spherical wavelets, which help in determining the new wavefront.

Example Problems

Example 1

Two plane mirrors intersect at right angles. A laser beam strikes the first of them at a point 11.5 $\mathrm{cm}$ from their point of intersection, as shown in Fig. 33.38 For what angle of incidence at the first mirror will this ray strike the midpoint of the second mirror (which is 28.0 $\mathrm{cm}$ long) after reflecting from the first mirror?

Example 2

Three plane mirrors intersect at right angles. A beam of laser light strikes the first of them at an angle $\theta$ with respect to the normal (Fig. 33.39$)$ . (a) Show that when this ray is reflected off of the other two mirrors and crosses the original ray, the angle $\alpha$ between these two rays will be $\alpha=180^{\circ}-2 \theta .$ (b) For what angle $\theta$ will the two rays be perpendicular when they cross?

Example 3

A beam of light has a wavelength of 650 nm in vacuum. (a) What is the speed of this light in a liquid whose index of refraction at this wavelength is 1.477 (b) What is the wavelength of these waves in the liquid?

Example 4

Light with a frequency of $5.80 \times 10^{14} \mathrm{Hz}$ travels in a block of glass that has an index of refraction of $1.52 .$ What is the wave-length of the light (a) in vacuum and (b) in the glass?

Example 5

A light beam travels at $1.94 \times 10^{8} \mathrm{m} / \mathrm{s}$ in quartz. The wave-length of the light in quartz is 355 $\mathrm{nm}$ . (a) What is the index of refraction of quartz at this wavelength? (b) If this same light travels through air, what is its wavelength there?
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Step-by-Step Explanations

QUESTION

How does light reflect off a surface, and what does the law of reflection state?

STEP-BY-STEP ANSWER:

Step 1: Identify the incident ray, which is the incoming light hitting the surface.
Step 2: Draw a normal line perpendicular to the surface at the point of incidence.
Step 3: Measure the angle between the incident ray and the normal; this is the angle of incidence.
Step 4: According to the law of reflection, the angle of reflection (the angle between the reflected ray and the normal) is equal to the angle of incidence.
Step 5: Draw the reflected ray such that it leaves the surface at an angle equal to the incident angle.
Final Answer: Light reflects off the surface such that the angle of incidence equals the angle of reflection.

Reflection

QUESTION

Explain the process of refraction and how Snell's law is used to determine the change in light's direction when passing from air to water.

STEP-BY-STEP ANSWER:

Step 1: Recognize that refraction occurs when light travels from one medium (e.g., air) to another (e.g., water), changing speed.
Step 2: Draw the incident ray approaching the interface, and the normal line at the point of incidence.
Step 3: Identify the angle of incidence (θ₁) and the angle of refraction (θ₂).
Step 4: Apply Snell's law, which is given by n₁*sin(θ₁) = n₂*sin(θ₂), where n₁ and n₂ are the refractive indices of the respective media.
Step 5: Solve for the unknown angle or index if other values are provided.
Final Answer: Light bends upon entering a new medium based on the ratio of the refractive indices of the two media, as described by Snell's law.

Refraction

QUESTION

How does Huygens's principle help explain the propagation of light waves?

STEP-BY-STEP ANSWER:

Step 1: Understand that Huygens's principle treats every point on a wavefront as a source of secondary spherical wavelets.
Step 2: Recognize that these secondary wavelets spread out in all directions from the point source.
Step 3: The new wavefront at a later time is determined by the tangent to all these secondary wavelets.
Step 4: Use the principle to predict how light waves will bend around obstacles or spread after passing through apertures.
Final Answer: Huygens's principle explains light propagation by considering each point on a wavefront as a source of new wavelets, thereby allowing the prediction of the wavefront’s future position.

Huygens's Principle

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Common Mistakes

  • Mixing up the distinct processes of reflection and refraction, or assuming they operate under the same principles.
  • Confusing the wave model with the particle model without recognizing the contexts in which each model is most applicable.
  • Overlooking the importance of Huygens's principle in explaining wave behavior, leading to an incomplete understanding of light propagation.
  • Misapplying Snell's law by not correctly identifying the normal or by using incorrect refractive index values.