The prism shown is made of glass with index of refraction 1.52. The light enters on the left parallel to the base of the prism. Determine the exit angle θ .\ Be very clear in showing your work.
The prism shown is made of glass with index of refraction 1.52. The light enters on the left parallel to the base of the prism. Determine the exit angle θ .\ Be very clear in showing your work.
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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The prism shown is made of glass with index of refraction 1.52. The light enters on the left parallel to the base of the prism. Determine the exit angle θ .\ Be very clear in showing your work.
![**Transcription and Explanation for Educational Website:**
**Diagram Overview:**
The diagram illustrates a triangle with labeled interior angles and an extended line intersecting one side of the triangle. Here is a detailed breakdown of the components:
1. **Triangle**:
- The triangle has three interior angles.
- The top angle of the triangle is labeled as \(54^\circ\).
- The two base angles of the triangle, on the left and right sides, are each labeled as \(63^\circ\).
2. **Extended Line and Exterior Angle**:
- An exterior line extends from one vertex on the left side of the triangle.
- This line forms an exterior angle labeled as \( \theta \) with the adjacent side of the triangle.
**Explanation:**
1. **Identification of Triangle Angles**:
- The triangle’s angles sum up to \(180^\circ\) as per the properties of a triangle.
- The angles are given as \(54^\circ\), \(63^\circ\), and \(63^\circ\).
2. **Exterior Angle**:
- The exterior angle \( \theta \) is formed by extending one side of the triangle.
- The exterior angle \( \theta \) is supplementary to the interior angle adjacent to it (which is \(63^\circ\)).
- According to the exterior angle theorem, the measure of this exterior angle can be calculated as the sum of the two opposite interior angles of the triangle:
\[
\theta = 54^\circ + 63^\circ = 117^\circ
\]
**Conclusion:**
This diagram is useful for visualizing key properties and theorems related to triangle angles and exterior angles. It exemplifies the rule that the exterior angle is equal to the sum of the two opposite interior angles, reinforcing the understanding of fundamental geometric principles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F093e8e2d-e528-490a-b84f-32f3af733c03%2F1536b9fa-5a5a-4cd1-b43b-856b3b2d652b%2Fk4kwmvo_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription and Explanation for Educational Website:**
**Diagram Overview:**
The diagram illustrates a triangle with labeled interior angles and an extended line intersecting one side of the triangle. Here is a detailed breakdown of the components:
1. **Triangle**:
- The triangle has three interior angles.
- The top angle of the triangle is labeled as \(54^\circ\).
- The two base angles of the triangle, on the left and right sides, are each labeled as \(63^\circ\).
2. **Extended Line and Exterior Angle**:
- An exterior line extends from one vertex on the left side of the triangle.
- This line forms an exterior angle labeled as \( \theta \) with the adjacent side of the triangle.
**Explanation:**
1. **Identification of Triangle Angles**:
- The triangle’s angles sum up to \(180^\circ\) as per the properties of a triangle.
- The angles are given as \(54^\circ\), \(63^\circ\), and \(63^\circ\).
2. **Exterior Angle**:
- The exterior angle \( \theta \) is formed by extending one side of the triangle.
- The exterior angle \( \theta \) is supplementary to the interior angle adjacent to it (which is \(63^\circ\)).
- According to the exterior angle theorem, the measure of this exterior angle can be calculated as the sum of the two opposite interior angles of the triangle:
\[
\theta = 54^\circ + 63^\circ = 117^\circ
\]
**Conclusion:**
This diagram is useful for visualizing key properties and theorems related to triangle angles and exterior angles. It exemplifies the rule that the exterior angle is equal to the sum of the two opposite interior angles, reinforcing the understanding of fundamental geometric principles.
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