Light

27.1 The Wave Aspect of Light: Interference

3 min read•june 18, 2024

Light behaves as both a particle and a wave, exhibiting properties like , , and speed. These characteristics explain how light interacts with objects, leading to phenomena such as reflection, refraction, , and interference.

Understanding light's wave nature is crucial for grasping its behavior in different media. The , which relates light's speed in vacuum to its speed in a medium, helps explain how light bends and changes wavelength when moving between materials.

Wave Behavior of Light

Wave properties of light

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Light exhibits wave-like properties characterized by wavelength ( $\lambda$ ), frequency ( $f$ ), speed ( $v$ ), and
Wavelength, frequency, and speed are related by the equation $v = \lambda f$
Speed of light varies in different media
- In vacuum, speed of light is $c = 3 \times 10^8$ m/s
- In other media, speed of light is $v = c/n$ , where $n$ is the (water, glass)
Wavelength changes in different media while frequency remains constant
- is given by $\lambda_n = \lambda_0 / n$ , where $\lambda_0$ is the wavelength in vacuum

Light interactions with objects

Ray behavior (geometric optics) occurs when object size is much larger than the wavelength of light
- Light travels in straight lines (rays) and explains reflection and refraction (mirrors, lenses)
Wave behavior (physical optics) occurs when object size is comparable to or smaller than the wavelength of light
- Diffraction is the bending of light around edges or through small openings
  - pattern consists of alternating bright and dark fringes
  - pattern creates an interference pattern with bright and dark fringes
- Interference is the of waves
  - occurs when waves are in , resulting in bright fringes
  - occurs when waves are out of phase, resulting in dark fringes

Wave characteristics and interference

Phase refers to the position of a wave in its cycle, affecting interference patterns
is the degree of correlation between waves, essential for producing stable interference patterns
describes the orientation of light waves' oscillations
, conducted by , demonstrates light's wave nature through interference

Interaction of Light with Matter

Index of refraction calculations

Index of refraction ( $n$ ) is the ratio of the speed of light in vacuum to the speed of light in a medium, given by $n = c / v$
Wavelength in a medium is calculated using $\lambda_n = \lambda_0 / n$ $λ_{n} = λ_{0} / n$
- Wavelength decreases when light enters a medium with a higher index of refraction (water to glass)
Speed of light in a medium is calculated using $v = c / n$ $v = c / n$
- Speed decreases when light enters a medium with a higher index of refraction (air to water)
relates the angles of incidence ( $\theta_1$ $θ_{1}$ ) and refraction ( $\theta_2$ $θ_{2}$ ) at the boundary between two media: $n_1 \sin \theta_1 = n_2 \sin \theta_2$ $n_{1} sin θ_{1} = n_{2} sin θ_{2}$
- Used to calculate the angle of refraction when light passes from one medium to another (air to water, glass to air)

Key Terms to Review (24)

Beat frequency: Beat frequency is the frequency at which two waves of slightly different frequencies interfere with each other, resulting in a modulation pattern perceived as a periodic variation in amplitude. It is calculated as the absolute difference between the frequencies of the two interfering waves.

Coherence: Coherence is a fundamental property of waves that describes the extent to which different parts of a wave or different waves maintain a fixed phase relationship with one another. It is a crucial concept in understanding the wave-like behavior of light and its applications in various areas of physics.

Constructive interference: Constructive interference occurs when two or more waves superpose to form a resultant wave with a greater amplitude than any of the individual waves. This happens when the phase difference between the waves is an integer multiple of $2\pi$ radians.

Constructive Interference: Constructive interference is a phenomenon that occurs when two or more waves, such as sound or light waves, interact and reinforce each other, resulting in an increase in the amplitude or intensity of the combined wave. This principle is fundamental to understanding various wave-related phenomena in physics, including superposition, interference, and diffraction.

De Broglie wavelength: The de Broglie wavelength is the wavelength associated with a particle and is inversely proportional to its momentum. It highlights the wave-particle duality of matter.

Destructive interference: Destructive interference occurs when two waves meet in such a way that their crests and troughs cancel each other out, resulting in a reduced or zero amplitude. This phenomenon is a result of the superposition principle.

Destructive Interference: Destructive interference occurs when two waves of the same frequency and amplitude interfere in such a way that they cancel each other out, resulting in a decrease or complete elimination of the wave amplitude at certain points. This phenomenon is observed in various wave-based systems, including sound, light, and electromagnetic waves.

Diffraction: Diffraction is the bending and spreading of waves as they encounter an obstacle or an aperture. This phenomenon occurs when waves, such as light or sound, encounter an edge or an opening, causing them to bend and spread out, rather than traveling in a straight line.

Direction of polarization: Direction of polarization refers to the orientation of the electric field vector in an electromagnetic wave. It describes how the electric field oscillates as the wave propagates.

Double-slit diffraction: Double-slit diffraction is a phenomenon that occurs when light or other waves pass through two closely spaced slits, resulting in an interference pattern of alternating bright and dark fringes on a screen. This behavior illustrates the wave nature of light, showcasing how waves can overlap and interfere with one another to create constructive and destructive interference.

Frequency: Frequency is a fundamental concept in physics that describes the number of occurrences of a repeating event per unit of time. It is a crucial parameter in various areas of study, including radiation, oscillations, waves, sound, and electromagnetic phenomena.

Index of refraction: The index of refraction, or refractive index, is a dimensionless number that describes how light propagates through a medium. It is defined as the ratio of the speed of light in a vacuum to its speed in the specified medium.

Index of Refraction: The index of refraction, also known as the refractive index, is a dimensionless number that describes how light propagates through a particular medium. It is a fundamental property of a material that determines the speed of light within that material and the degree to which light is bent, or refracted, when it passes from one medium to another.

Phase: Phase refers to the position of a wave in its cycle, typically measured as the angle or fraction of a complete oscillation. It is a crucial concept in understanding the behavior of waves, such as their interference and diffraction patterns.

Polarization: Polarization is a fundamental property of electromagnetic waves, including light, that describes the orientation of the electric field oscillations within the wave. It is a crucial concept that underlies many important phenomena in the fields of static electricity, electromagnetism, and optics.

Single-Slit Diffraction: Single-slit diffraction is a phenomenon in which a beam of light or other waves passing through a single narrow slit exhibits a diffraction pattern on a screen or surface placed beyond the slit. This pattern is characterized by a central bright region surrounded by alternating bright and dark bands, known as interference fringes.

Snell's Law: Snell's law, also known as the law of refraction, describes the relationship between the angles of incidence and refraction when light passes from one medium to another with a different refractive index. It is a fundamental principle in the study of optics and the behavior of light.

Superposition: Superposition is the principle that when two or more waves overlap, the resulting wave displacement is the sum of the individual wave displacements. This principle applies to all types of waves, including mechanical and electromagnetic.

Superposition: Superposition is the principle that when two or more waves or oscillations occur at the same time and location, their net displacement is the vector sum of the individual displacements. This concept is fundamental to the understanding of various wave phenomena, including interference and diffraction.

Thomas Young: Thomas Young was a renowned British polymath who made significant contributions to the fields of optics, wave theory, and surface tension. His work laid the foundations for our understanding of the wave nature of light and the principles of interference, diffraction, and thin-film interference.

Wave Amplitude: The wave amplitude is the maximum displacement of a wave from its resting position. It represents the maximum amount of disturbance or oscillation in a wave and is a fundamental characteristic that describes the strength or intensity of a wave.

Wavelength: Wavelength is a fundamental characteristic of waves, representing the distance between consecutive peaks or troughs in a wave. It is a crucial parameter that describes the spatial extent of a wave and is closely related to other wave properties such as frequency and speed.

Wavelength in a medium: Wavelength in a medium is the distance between successive crests or troughs of a wave as it propagates through that medium. It varies depending on the properties of the medium and the frequency of the wave.

Young's Double-Slit Experiment: Young's double-slit experiment is a classic demonstration of the wave nature of light, where the interference of light waves passing through two narrow slits produces a characteristic pattern of bright and dark regions on a screen. This experiment provided evidence that light exhibits properties of waves, rather than just particles.

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Glossary

27.1 The Wave Aspect of Light: Interference

Wave Behavior of Light

Wave properties of light

Top images from around the web for Wave properties of light

Top images from around the web for Wave properties of light

Light interactions with objects

Wave characteristics and interference

Interaction of Light with Matter

Index of refraction calculations

Key Terms to Review (24)

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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

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27.2 Huygens's Principle: Diffraction