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Chapter 21: Problem 10

Briefly describe the phenomenon of dispersion in a transparent medium.

Short Answer

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Short Answer: Dispersion is a phenomenon that occurs when light passes through a transparent medium, causing the separation of different wavelengths (colors) as they travel at different speeds within the medium. This separation of colors occurs due to the variation in the refractive index of the medium for different wavelengths. The visible light spectrum, which includes colors ranging from violet to red, is created when a beam of light passes through a dispersive medium, such as a prism, and each wavelength refracts differently to reveal individual colors.

Step by step solution

01

Understanding Dispersion

Dispersion occurs when light passes through a transparent medium (such as glass, water, or air), causing the different wavelengths of light to travel at different speeds. This results in the separation of colors in the light. The cause of this phenomenon is the variation of the refractive index of the medium with respect to the different wavelengths of light.
02

Behavior of Wavelengths in a Medium

When light enters a medium, the speed of each wavelength (color) gets affected by the medium's properties. Typically, shorter wavelengths (blue/violet) slow down more than longer wavelengths (red/orange), because they are more attracted to the medium's molecules. This causes the different wavelengths to refract differently, and thus, the separation of colors.
03

Refractive Index and Wavelengths

The degree of refraction of each light wavelength in the medium is determined by the refractive index of the medium. The refractive index of a medium usually decreases as the wavelength of the light increases, which means violet light (shorter wavelength) is refracted more than red light (longer wavelength) and the colors spread out. This relationship can be described using an equation called Cauchy's Equation: \[n = A + \frac{B}{\lambda^2}\] where n is the refractive index, A and B are constants specific to the medium, and 位 is the wavelength of the light.
04

The Visible Light Spectrum

When a beam of light passes through a prism or other dispersive medium, the refraction of different wavelengths creates a continuous spread of colors, known as the visible light spectrum. It ranges from violet (shortest wavelength, ~400 nm) to red (longest wavelength, ~700 nm). This visible light spectrum is the result of the dispersion phenomenon in transparent media. White light, like sunlight, contains all the colors of the visible light spectrum, which is why we see a rainbow of colors when sunlight passes through a prism.

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