Index of refraction related to wavelength & frequency

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The discussion centers on the relationship between the index of refraction, wavelength, and frequency in light. It clarifies that while frequency remains constant when light crosses a boundary, the wavelength changes, affecting the index of refraction. The formula n = c/v indicates that a smaller wavelength results in a larger index of refraction, leading to greater bending of light. Specifically, violet light, with a shorter wavelength, has a higher index of refraction than red light, causing it to bend more when passing through a prism. Understanding this relationship is crucial for grasping concepts of light behavior in optics.
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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