Index of refraction related to wavelength & frequency

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SUMMARY

The discussion centers on the relationship between the index of refraction (n), wavelength (λ), and frequency (f) of light, particularly in the context of dispersion as described in Kaplan's MCAT prep material. It is established that the index of refraction is defined by the equation n = c/v, where c is the speed of light and v is the speed of light in a medium. The confusion arises from the fact that while frequency remains constant when light transitions between media, the wavelength changes, leading to the conclusion that shorter wavelengths (like violet light) experience a higher index of refraction and greater bending compared to longer wavelengths (like red light).

PREREQUISITES
  • Understanding of the speed of light (c) and its relationship with wavelength (λ) and frequency (f).
  • Familiarity with the concept of index of refraction (n) and its calculation.
  • Basic knowledge of wave behavior, particularly in optics.
  • Concept of dispersion and its effects on light passing through different media.
NEXT STEPS
  • Study the principles of light dispersion using prisms and how different wavelengths are affected.
  • Explore the mathematical relationship between frequency, wavelength, and speed of light in various media.
  • Investigate the implications of the index of refraction in optical devices such as lenses and fiber optics.
  • Learn about the phenomenon of chromatic aberration and its relevance in optics.
USEFUL FOR

Students preparing for the MCAT, educators teaching optics, and anyone interested in the fundamental principles of light behavior and its applications in physics and engineering.

reshmaji
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I'm going through the Light & Optics chapter of Kaplan MCAT prep material & am having a hard time conceptually understanding the relationship between index of refraction & wavelength or with frequency.

It says in the book that n = c/v, & "when the speed of the light wave varies with wavelength, a material exhibits dispersion", then goes on to describe white light dispersion by a prism. Here is where I get confused, it continues to state that "violet light 'sees' a greater index of refraction than red does & so is bent to a greater extent"

The book also clearly indicates that larger f = smaller λ = larger n = more bending (e.g. for violet light relative to red). How is that so? Considering that v = fλ, smaller λ corresponds to smaller v & so by n = c/v it also corresponds to larger n & more bending, but shouldn't larger f = larger v = smaller n??

Any help would be appreciated! :)
 
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This is a good question. The frequency of the light doesn't actually change when the light crosses a boundary, only the wavelength does. Thus n = c/v = c/(fλ) and is thus inversely proportional to the wavelength.
 
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