A narrow beam of white light strikes one face of a slab of...

A narrow beam of white light strikes one face of a slab of silicate flint glass. The light is traveling parallel to the two adjoining faces, as shown in $\textbf{Fig. E33.23}$. For the transmitted light inside the glass, through what angle $\Delta \theta$ is the portion of the visible spectrum between 400 nm and 700 nm dispersed? (Consult the graph in Fig. 33.17.)

A narrow beam of white light strikes one face of a slab of silicate flint glass. The light is traveling parallel to the two adjoining faces, as shown in $\textbf{Fig. E33.23}$. For
the transmitted light inside the glass, through what angle $\Delta \theta$ is the portion of the visible spectrum between 400 nm and 700 nm dispersed? (Consult the graph in Fig. 33.17.)

Key Concepts

Visible Spectrum

The visible spectrum is the range of electromagnetic wavelengths that can be detected by the human eye, typically ranging from about 400 nanometers (violet) to 700 nanometers (red). Understanding the visible spectrum is important in problems involving the dispersion of light, as it defines the range within which the dispersion effects are observed.

Angular Dispersion

Angular dispersion refers to the change in the angle of deviation with respect to wavelength. In a material where the refractive index changes with wavelength, light of different wavelengths will exit the medium at slightly different angles. This concept is used to quantify how widely the colors in the visible spectrum are spread after passing through a dispersive element.

Refractive Index

The refractive index of a medium is a measure of how much light slows down when entering that medium compared to its speed in a vacuum. In dispersive materials, the refractive index depends on the wavelength of the light, which is crucial for understanding how and why different wavelengths bend by different amounts.

Dispersion

Dispersion is the optical phenomenon where different wavelengths of light travel at different speeds in a medium, leading to a variation in their refractive indices. This variation causes the various colors in white light to refract by different amounts, resulting in the spread or separation of colors when light passes through materials such as glass or a prism.

Snell's Law

Snell's Law describes how light is refracted at the boundary between two media with different refractive indices. It states that the product of the refractive index and the sine of the angle of incidence in the first medium equals that in the second medium. This relationship is fundamental in calculating the angles at which different wavelengths of light propagate through a medium.

Transcript

00:01 In this question we have white light shining on silicate flints glass.

00:05 We want to find out the angle delta data between the 400 nanometer and 700 nanometer dispersed.

00:15 So this is about dispersion, okay, and we know that the refractive index changes with the wavelength of the visible light.

00:25 So from the graph, okay, we found that at, lambda equals to 400 nanometers, the refractive index is 1 .66, and then at lambda equals to 700 nanometer, then refractive index is 1 .6.

00:45 Okay, so this is from figure to 3 .17.

00:53 So to find, so we have a refraction taking place.

00:59 So we need to label the angle of so the here is 55 degrees and we have 35 degrees over here.

01:10 Okay.

01:12 So the angle or refraction for each one, okay, it will be labeled here.

01:26 This is the data r.

01:28 So the delta data is the is the refractive angle, angle of reflection of red light minus the angle of reflection of blue light.

01:44 Okay.

01:46 Okay.

01:47 So for lambda or wireless light, okay, not blue, but violet.

01:57 Okay, so for lambda it goes to 400 nanometers, okay, and then we calculate the n is 1 .66 then using snal's law, now gives us, side, okay, so the refractive index of air times side 35 degrees equals to 1 .66, side data are pilot.

02:31 Okay, so just to mention snell's law, here we have n1, sine data 1 equals 2, and 2, side data 2...

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