A horizontal incident beam consisting of white light passes...

A horizontal incident beam consisting of white light passes through an equilateral prism, like the one shown in Figure $26-$ 69. What is the dispersion $\left(\theta_{v}-\theta_{r}\right)$ of the outgoing beam if the prism's index of refraction is $n_{v}=1.505$ for violet light and $n_{r}=1.421$ for red light?

A horizontal incident beam consisting of white light passes through an equilateral prism, like the one shown in Figure $26-$
69. What is the dispersion $\left(\theta_{v}-\theta_{r}\right)$ of the outgoing beam if
the prism's index of refraction is $n_{v}=1.505$ for violet light and
$n_{r}=1.421$ for red light?

Key Concepts

Prism Deviation

Prism deviation is the change in direction of a light beam as it passes through a prism, which is influenced by the prism’s geometry and the refractive indices for different wavelengths. The deviation depends on the incident angle, the prism’s apex angle, and the refractive index, which causes different wavelengths to deviate by different amounts. This differential bending is what leads to the separation of light into a spectrum, a critical aspect in the study of optics and the practical applications of prisms.

Optical Dispersion

Optical dispersion refers to the phenomenon in which different wavelengths of light refract by different amounts when passing through a medium. This occurs because the medium’s refractive index varies with wavelength, causing colors such as violet and red to deviate by different angles. Dispersion is a fundamental concept in explaining how white light can be separated into its constituent colors, as seen in prisms and similar optical devices.

Snell’s Law

Snell’s Law governs the refraction of light at the interface between two media with different refractive indices. It mathematically relates the angle of incidence to the angle of refraction with respect to the refractive indices of the respective media. Understanding this law is essential for determining how light will be bent as it passes through a prism, which in turn influences the angular deviation that results in dispersion.

Transcript

00:01 In this question, a horizontal beam enters an equilateral prism.

00:08 Okay, and so, and that horizontal beam is a white light.

00:14 So it has the rainbow colors, but we want to find the extreme dispersion.

00:21 So we want to calculate the angle that violet light, the outgoing beam of the out of violet light, the distribution of the outgoing b.

00:32 So the theta violet minus the data rate.

00:36 And we are given that the refractive index of the violet light in glass is 1 .505 and then the violet, the refractive index for red light in glass is 1 .421.

00:53 So the rate diagram for both for both the so the diagram shown over here is the dispersion of the white light of course we expect the angle to be different for wireless light and red light so so i'm just going to label the general angles so this is data 1, data 2, data 3, and data four.

01:32 Okay, those are the key angles that we encounter in this as light passes through this equilateral prism and then we also have this angle which is 120 degrees came this which gives us data 2 plus data 3 equals to 60 degrees right so that's something that is useful going to be used in the question when we solve the problem.

01:59 Okay so and yeah so to find the answer we will be using snail's law a lot in this case okay so solution okay so we have uh now slow okay basically saying that uh n1 side data 1 is equal to and 2 side data 2 then and 2 side data 3 is equal to n and 1 side data 4 okay so n1 is air and 2 is the refractive index indices for read or weather lights okay there's something that will labor with a subscript.

03:07 Then and at the same time data 1 is 30 degrees.

03:13 Yeah...

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