∙Light inside the eye. The vitreous humor, a transparent,...

$\bullet$ Light inside the eye. The vitreous humor, a transparent, gelatinous fluid that fills most of the eyeball, has an index of refraction of 1.34 . Visible light ranges in wavelength from 400 $\mathrm{nm}$ (violet) to $700 \mathrm{nm}(\mathrm{red}),$ as measured in air. This light travels through the vitreous humor and strikes the rods and cones at the surface of the retina. What are the ranges of (a) the wavelength, (b) the frequency, and (c) the speed of the light just as it approaches the retina within the vitreous humor?

$\bullet$ Light inside the eye. The vitreous humor, a transparent, gelatinous fluid that fills most of the eyeball, has an index of refraction of 1.34 . Visible light ranges in wavelength from
400 $\mathrm{nm}$ (violet) to $700 \mathrm{nm}(\mathrm{red}),$ as measured in air. This light travels through the vitreous humor and strikes the rods and cones at the surface of the retina. What are the ranges of (a) the wavelength, (b) the frequency, and (c) the speed of the light just as it approaches the retina within the vitreous humor?

Key Concepts

Visible Spectrum

The visible spectrum of light encompasses wavelengths ranging from approximately 400 nm (violet) to 700 nm (red). These values are typically given for light in air, and when light passes into a medium like the vitreous humor, adjustments in wavelength are considered while the frequency remains unchanged.

Index of Refraction

The index of refraction is a dimensionless quantity that expresses the ratio of the speed of light in a vacuum to its speed in a medium. It determines how much light slows down when it enters that medium, with higher values meaning slower light speeds.

Wavelength in a Medium

When light enters a medium, its wavelength decreases in proportion to the medium’s index of refraction. The relationship is given by ?_medium = ?_air/n, meaning that the wavelength in a medium is the wavelength in air divided by the index of refraction.

Frequency Invariance

Frequency remains constant when light transitions from one medium to another. Although both the wavelength and speed of light change when entering a different medium, the frequency is set by the light source and does not vary with the medium.

Speed of Light in a Medium

The speed of light in any medium is determined by the formula v = c/n, where c is the speed of light in vacuum and n is the medium's index of refraction. Thus, light travels slower in media with a refractive index greater than one.

Transcript

00:01 Let's first figure out what the wavelength of violet light is inside the eyeball.

00:06 And so the lambda of violet light is equal to the lambda not over the index of a fraction.

00:15 And this is lambda not of violet light divided by the index over fraction of the fluid inside the eye.

00:22 And so this is equal to 400 nanometers.

00:25 And we're told the index is 1 .34.

00:30 And so this gives 299 nanometers.

00:35 Similarly, we're going to do it for red light.

00:39 So this equals lambda not, but for red light over the index of a fraction.

00:45 And so this is 700 now, 700 nanometers over 1 .34.

00:52 And so this gives 522 nanometers.

00:57 And so this is the range here, from 299 to 522 nanometers.

01:04 For b, we need to figure out the range in frequencies.

01:08 So to do this, we're going to use the formula that the frequency is the speed over the wavelength.

01:16 And we just calculate what the wavelengths were.

01:20 And so let's figure out what the frequency for biolitis.

01:23 It's equal to the c over lambda v.

01:29 And so it's equal to 3 times 10 to the 8 meters per second over 299 nanometers.

01:38 And before you do this calculation out, make sure that you convert the 299 nanometers into meters...

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