A beam of light with red and blue components of wavelengths 670 nm and 425 nm, respectively, str

Name: Problem 45, Chapter 22: College Physics
Uploaded: 2021-05-12T02:53:48-08:00
Duration: 2 min 43 s
Channel: Narayan Hari
Description: A beam of light with red and blue components of wavelengths 670 nm and 425 nm, respectively, strikes a slab of fused quartz at an incident angle of 30^∘ . On refraction, the different components are separated by an angle of 0.00131 rad. If the index of refraction of the red light is 1.4925, what is the index of refraction of the blue light?

step 1 In this problem, we have given the wavelength of the red light, lambda r is equal to 670 nm. Lam

Question

A beam of light with red and blue components of wavelengths $670 \mathrm{nm}$ and $425 \mathrm{nm}$, respectively, strikes a slab of fused quartz at an incident angle of $30^{\circ} .$ On refraction, the different components are separated by an angle of 0.00131 rad. If the index of refraction of the red light is $1.4925,$ what is the index of refraction of the blue light?

   A beam of light with red and blue components of wavelengths $670 \mathrm{nm}$ and $425 \mathrm{nm}$, respectively, strikes a slab of fused quartz at an incident angle of $30^{\circ} .$ On refraction, the different components are separated by an angle of 0.00131 rad. If the index of refraction of the red light is $1.4925,$ what is the index of refraction of the blue light?

College Physics

Jerry D. Wilson,… 7th Edition

Chapter 22, Problem 45

Instant Answer

Solved by Expert Narayan Hari

05/12/2021

Step 1

The angle of incidence, $\theta_i = 30^{\circ}$, and the refractive index of the red light, $n_R = 1.4925$. The angle between the refracted red and blue light is given as $0.00131 \, rad$. Show more…

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A beam of light with red and blue components of wavelengths $670 \mathrm{nm}$ and $425 \mathrm{nm}$, respectively, strikes a slab of fused quartz at an incident angle of $30^{\circ} .$ On refraction, the different components are separated by an angle of 0.00131 rad. If the index of refraction of the red light is $1.4925,$ what is the index of refraction of the blue light?

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Key Concepts

Optical Dispersion

Optical dispersion refers to the dependence of a material's refractive index on the wavelength (or color) of light. In dispersive media, different colors of light travel at different speeds, leading to different bending angles upon refraction. This concept explains phenomena such as the separation of white light into its constituent colors by a prism, and is essential in understanding how and why light components of different wavelengths refract at slightly different angles.

Snell's Law

Snell's law relates the angles of incidence and refraction to the refractive indices of two media. It is a fundamental principle of optics that describes how light bends when it passes from one transparent medium to another. The law is mathematically expressed as n? sin?? = n? sin??, where n? and n? are the refractive indices of the initial and secondary media, and ?? and ?? are the angles of incidence and refraction, respectively.

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