A ray of light is incident normally on one of the faces of a prism of index of refraction n = 1.49. The ray emerges out of the prism with an angle of refraction e equal to:
A ray of light is incident normally on one of the faces of a prism of index of refraction n = 1.49. The ray emerges out of the prism with an angle of refraction e equal to:
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![**Refraction Through a Prism**
A ray of light is incident normally on one of the faces of a prism with an index of refraction \( n = 1.49 \). The ray emerges out of the prism with an angle of refraction \( \theta \) equal to:
The diagram shows a prism with an apex angle of 50°, and the following labels:
- The incident angle \( \alpha \) on both sides of the prism.
- The index of refraction for air, \( n_{\text{air}} = 1 \).
- The index of refraction for the prism material, \( n = 1.49 \).
- The angle inside the prism as the ray moves through it, labeled \( \beta \).
- The ray emerging out of the prism at an angle \( \theta \).
### Detailed Diagram Description:
- The prism is a triangle with one angle labeled 50°.
- A ray of light enters the prism at a right angle to one face, traveling straight through the medium.
- As it reaches the second face, it bends towards the normal due to the change in medium.
- The emerging angle is designated as \( \theta \).
### Question:
Using the diagram and the provided indices of refraction, determine the angle of refraction \( \theta \).
### Options:
1. 21.4°
2. 24.0°
3. 22.7°
4. 20.2°
5. 26.8°
### Explanation of Refraction:
Refraction occurs when light passes from one medium to another, changing its speed and thereby altering its path according to Snell's Law, which is given by:
\[ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \]
Where \( n_1 \) and \( n_2 \) are the indices of refraction for the two media, and \( \theta_1 \) and \( \theta_2 \) are the angles of incidence and refraction respectively.
**Answer Calculation:**
Given the specific indices of refraction for air and the prism, and the geometry of the prism provided, you would typically use trigonometric relationships and Snell's Law to solve for the unknown angle \( \theta \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ee83936-8eac-4b06-a9d3-229c21966046%2F28ba7028-cfbf-4502-b2cf-8fac9f21208c%2Fso7ddrh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Refraction Through a Prism**
A ray of light is incident normally on one of the faces of a prism with an index of refraction \( n = 1.49 \). The ray emerges out of the prism with an angle of refraction \( \theta \) equal to:
The diagram shows a prism with an apex angle of 50°, and the following labels:
- The incident angle \( \alpha \) on both sides of the prism.
- The index of refraction for air, \( n_{\text{air}} = 1 \).
- The index of refraction for the prism material, \( n = 1.49 \).
- The angle inside the prism as the ray moves through it, labeled \( \beta \).
- The ray emerging out of the prism at an angle \( \theta \).
### Detailed Diagram Description:
- The prism is a triangle with one angle labeled 50°.
- A ray of light enters the prism at a right angle to one face, traveling straight through the medium.
- As it reaches the second face, it bends towards the normal due to the change in medium.
- The emerging angle is designated as \( \theta \).
### Question:
Using the diagram and the provided indices of refraction, determine the angle of refraction \( \theta \).
### Options:
1. 21.4°
2. 24.0°
3. 22.7°
4. 20.2°
5. 26.8°
### Explanation of Refraction:
Refraction occurs when light passes from one medium to another, changing its speed and thereby altering its path according to Snell's Law, which is given by:
\[ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \]
Where \( n_1 \) and \( n_2 \) are the indices of refraction for the two media, and \( \theta_1 \) and \( \theta_2 \) are the angles of incidence and refraction respectively.
**Answer Calculation:**
Given the specific indices of refraction for air and the prism, and the geometry of the prism provided, you would typically use trigonometric relationships and Snell's Law to solve for the unknown angle \( \theta \).
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