Glossary

25.3 The Law of Refraction

3 min read•june 18, 2024

Light bends when it moves between different materials. This bending, called , follows . Understanding refraction helps explain everyday phenomena like why objects appear bent in water or how rainbows form.

The changes in different materials, which affects how much it bends. This relationship is described by the . Knowing how light behaves in various materials is key to understanding optical devices and natural light phenomena.

The Law of Refraction

Angle of refraction calculation

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  • Snell's law relates (θ1\theta_1) and (θ2\theta_2) when light passes through boundary between two media with different (n1n_1 and n2n_2)
    • Snell's law: n1sin⁡θ1=n2sin⁡θ2n_1 \sin \theta_1 = n_2 \sin \theta_2
    • Example: Light passing from air (n1=1n_1 = 1) to water (n2=1.33n_2 = 1.33)
  • Calculate angle of refraction:
    1. Determine indices of refraction for two media (n1n_1 and n2n_2)
    2. Measure angle of incidence (θ1\theta_1) relative to
    3. Rearrange Snell's law to solve for θ2\theta_2: θ2=arcsin⁡(n1n2sin⁡θ1)\theta_2 = \arcsin(\frac{n_1}{n_2} \sin \theta_1)
  • Light bends towards normal line when traveling from lower to higher medium (air to water)
  • Light bends away from normal line when traveling from higher to lower index of refraction medium (water to air)
  • Snell's law is named after , who formulated it in 1621

Light speed in materials

  • Speed of light in (cc) approximately 3×1083 \times 10^8 m/s
  • In any other medium, speed of light (vv) slower than in vacuum
  • Index of refraction (nn) of medium is ratio of speed of light in vacuum to speed of light in that medium: n=cvn = \frac{c}{v}
    • Higher index of refraction indicates slower speed of light in medium (diamond, n=2.42n = 2.42)
    • Lower index of refraction indicates faster speed of light in medium (air, n=1n = 1)
  • Speed of light in medium related to its
    • Optically denser media have higher indices of refraction and slower light speeds (glass)
    • Optically less dense media have lower indices of refraction and faster light speeds (air)

Applications of Snell's law

  • Identify two media involved and their respective indices of refraction (n1n_1 and n2n_2)
  • Determine angle of incidence (θ1\theta_1) and whether angle of refraction (θ2\theta_2) or index of refraction of second medium (n2n_2) is unknown
  • If angle of refraction unknown:
    • Use Snell's law to calculate θ2\theta_2: θ2=arcsin⁡(n1n2sin⁡θ1)\theta_2 = \arcsin(\frac{n_1}{n_2} \sin \theta_1)
    • Example: Light passing from air (n1=1n_1 = 1) to water (n2=1.33n_2 = 1.33) at 30° angle of incidence
  • If index of refraction of second medium unknown:
    • Rearrange Snell's law to solve for n2n_2: n2=n1sin⁡θ1sin⁡θ2n_2 = \frac{n_1 \sin \theta_1}{\sin \theta_2}
    • Example: Light passing from air to unknown medium at 45° angle of incidence, refracted at 30°
  • Special cases:
    • occurs when light travels from higher to lower index of refraction medium at (θc\theta_c)
      • : θc=arcsin⁡(n2n1)\theta_c = \arcsin(\frac{n_2}{n_1})
      • Example: Light traveling from water to air at angles greater than 48.8°
    • No refraction at normal incidence (0°), light continues in straight line

Additional Optical Phenomena

  • : Separation of white light into its component colors due to -dependent refraction
  • of light remains constant during refraction, while wavelength changes in different media
  • : Process by which light waves are restricted to vibrate in a single plane

Key Terms to Review (25)

Angle of Incidence: The angle of incidence is the angle at which a ray of light or other wave strikes a surface. It is the angle between the incident ray and the normal (perpendicular) to the surface at the point of incidence. This term is crucial in understanding the behavior of light and waves as they interact with different mediums and surfaces.
Angle of refraction: The angle of refraction is the angle formed between the refracted ray and the normal line at the boundary of two different media when light passes from one medium to another. This angle is a result of the change in speed of light as it moves between materials with different optical densities, leading to a bending effect. Understanding this concept is essential for analyzing how light behaves when it enters various substances, impacting applications in optics, such as lenses and prisms.
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.
Critical angle: The critical angle is the minimum angle of incidence at which light is totally internally reflected within a medium. It occurs when light passes from a medium with a higher refractive index to one with a lower refractive index.
Critical Angle: The critical angle is the angle of incidence at which the angle of refraction becomes 90 degrees, marking the boundary between refraction and total internal reflection. It is a fundamental concept in the study of light and its behavior at the interface between two different media.
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.
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.
Dispersion: Dispersion is the phenomenon where light is separated into its constituent wavelengths or colors as it passes through a medium with a varying refractive index, such as a prism or the atmosphere. This separation of light occurs due to the fact that different wavelengths of light travel at slightly different speeds within the medium, causing them to bend at different angles.
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.
Indices of refraction: Indices of refraction, or refractive indices, are numerical values that describe how light propagates through different media. They indicate the ratio of the speed of light in a vacuum to the speed of light in a particular medium, influencing how much light bends or changes direction when it enters or exits different substances. Understanding indices of refraction is essential for analyzing optical phenomena such as refraction, reflection, and the behavior of lenses.
Law of refraction: The Law of Refraction, or Snell's Law, describes how light bends when it passes from one medium into another. It is mathematically expressed as $n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$, where $n$ is the refractive index and $\theta$ is the angle of incidence or refraction.
Law of Refraction: The law of refraction, also known as Snell's law, describes the relationship between the angles of incidence and refraction when light passes from one medium to another with a different refractive index. It governs the bending of light as it travels from one transparent material to another.
Normal Line: The normal line, also known as the normal, is a line that is perpendicular to a surface at a given point. It is a fundamental concept in the study of optics, particularly in the context of the law of refraction, as it helps determine the angle of refraction when light passes from one medium to another with a different refractive index.
Optical Density: Optical density is a measure of the absorption or attenuation of light as it passes through a medium. It is a dimensionless quantity that quantifies the degree to which a material or substance inhibits the transmission of light, and is an important concept in the understanding of the behavior of light in various contexts, including the Law of Refraction and the phenomenon of Dispersion.
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.
Refraction: Refraction is the bending of light as it passes from one medium to another with a different refractive index. This occurs due to the change in light's speed in different media.
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.
Speed of Light: The speed of light is the maximum velocity at which all electromagnetic radiation, including visible light, can travel through a vacuum. It is a fundamental constant of nature that plays a crucial role in various areas of physics, from Maxwell's equations to general relativity.
Total internal reflection: Total internal reflection occurs when a light wave traveling through a denser medium hits the boundary with a less dense medium at an angle greater than the critical angle, causing the wave to be completely reflected back into the denser medium. This phenomenon is critical in fiber optics and certain optical instruments.
Total Internal Reflection: Total internal reflection is a fundamental optical phenomenon that occurs when light encounters the boundary between two materials with different refractive indices, resulting in the light being completely reflected back into the original medium instead of passing through the boundary. This principle is crucial in understanding the behavior of light in various optical systems and applications.
Vacuum: A vacuum is a region of space that is essentially devoid of matter, with extremely low pressure and density. It is an environment that lacks any particles, whether they are gas, liquid, or solid. Vacuums are an important concept in the context of the Law of Refraction, as they play a crucial role in the behavior of light and other forms of electromagnetic radiation.
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.
Willebrord Snellius: Willebrord Snellius was a 17th-century Dutch mathematician and physicist who is best known for his formulation of the law of refraction, which describes the relationship between the angles of incidence and refraction of light passing through the interface between two different media.
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