**Problem Statement:**2. White light is incident from air onto an equiangular triangle prism at a 40.0° angle with respect to the normal. The prism is composed of crystal that has an index of refraction of 1.40 for red light and 1.45 for violet light. Take \( n_{\text{air}} = 1.00 \) for all wavelengths.**Question:**a. What is the angular separation of the red and violet ends of the spectrum within the prism?---**Explanation for Educational Context:**When light passes through a prism, it is refracted at the surfaces due to the change in speed as it moves from one medium to another. An equiangular triangle prism disperses the light, separating it into its component colors due to varying indices of refraction for different wavelengths. This phenomenon is called dispersion. In this problem, we are asked to determine the angular separation between the red and violet ends of the spectrum as they emerge from the prism.**Methodology Overview:**1. **Snell's Law:** Use Snell's Law to determine the angle of refraction inside the prism for both red and violet light: \[ n_{\text{air}} \cdot \sin(\theta_{\text{air}}) = n_{\text{prism}} \cdot \sin(\theta_{\text{prism}}) \]2. **Calculation of Deviation:** Calculate the angle of deviation for both red and violet light by considering the geometry of the prism and applying the refractive indices.3. **Angular Separation:** The difference between the angles of deviation for red and violet light gives the angular separation.This exercise demonstrates the fundamental principles of optics, specifically how prisms can separate white light into its constituent colors through refraction and dispersion.

according to Snell's law μ = Sin i / Sin r

respect to the normal. The prism is composed of crystal that has an index of refraction of 1.40 for red light and 1.45 for violet light. Take nair = 1.00 for all wavelengths. a. What is the angular separation of the red and violet ends of the spectrum within the prism?

respect to the normal. The prism is composed of crystal that has an index of refraction of 1.40 for red light and 1.45 for violet light. Take nair = 1.00 for all wavelengths. a. What is the angular separation of the red and violet ends of the spectrum within the prism?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Interference of Light

The word "constructive" signifies addition in interference. Constructive interference occurs when the path of the waves that start from the slit differs by 1 entire wavelength or in the intervals of the same. Hence, the waves that are presented on the screen are in phase (crest to crest/trough to trough). The waves interfering constructively forms bright fringes on the screen.

Question

**Problem Statement:**

2. White light is incident from air onto an equiangular triangle prism at a 40.0° angle with respect to the normal. The prism is composed of crystal that has an index of refraction of 1.40 for red light and 1.45 for violet light. Take \( n_{\text{air}} = 1.00 \) for all wavelengths.

**Question:**

a. What is the angular separation of the red and violet ends of the spectrum within the prism?

---

**Explanation for Educational Context:**

When light passes through a prism, it is refracted at the surfaces due to the change in speed as it moves from one medium to another. An equiangular triangle prism disperses the light, separating it into its component colors due to varying indices of refraction for different wavelengths. This phenomenon is called dispersion. In this problem, we are asked to determine the angular separation between the red and violet ends of the spectrum as they emerge from the prism.

**Methodology Overview:**

1. **Snell's Law:** Use Snell's Law to determine the angle of refraction inside the prism for both red and violet light:
\[
n_{\text{air}} \cdot \sin(\theta_{\text{air}}) = n_{\text{prism}} \cdot \sin(\theta_{\text{prism}})
\]

2. **Calculation of Deviation:** Calculate the angle of deviation for both red and violet light by considering the geometry of the prism and applying the refractive indices.

3. **Angular Separation:** The difference between the angles of deviation for red and violet light gives the angular separation.

This exercise demonstrates the fundamental principles of optics, specifically how prisms can separate white light into its constituent colors through refraction and dispersion.

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