A ray of light passes into and out of a glass prism as shown in the diagram. Find the refractive index of glass? A B O 1.52 O 1.54 O 1.5 O 1.49 41.7° C

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### Refraction in a Glass Prism

**Problem Statement:**

*A ray of light passes into and out of a glass prism as shown in the diagram. Find the refractive index of the glass?*

**Diagram Explanation:**

The diagram depicts a triangular glass prism labeled at vertices A, B, and C. The angle at vertex A measures 41.7 degrees. A ray of light enters the prism from the left side, bends due to refraction, and exits from the other side, following the law of refraction.

1. **Label A**: Apex of the prism with an angle of 41.7°.
2. **Label B and C**: The base vertices of the prism.
3. **Red Line**: Path of the light ray as it enters and exits the prism.
4. **Right Angle**: There is a right angle at vertex B.

**Given Options:**

- ⭘ 1.52
- ⭘ 1.54
- ⭘ 1.5
- ⭘ 1.49

By using Snell's Law and trigonometric calculations with the given angle:

**Snell's Law:**
\[ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \]

Where:
- \( \theta_1 \) and \( \theta_2 \) are the angles of incidence and refraction, respectively.
- \( n_1 \) is the refractive index of the air (approximately 1).
- \( n_2 \) is the refractive index of the glass.

Using the apex angle and right-axis triangular relationship, the incident and refraction angles can also be calculated. Students may need additional steps to solve the problem precisely.

Explore and choose the correct refractive index from the given options!

For more detailed solution steps and understanding the principles, ensure to refer to your textbooks or educational resources.
Transcribed Image Text:### Refraction in a Glass Prism **Problem Statement:** *A ray of light passes into and out of a glass prism as shown in the diagram. Find the refractive index of the glass?* **Diagram Explanation:** The diagram depicts a triangular glass prism labeled at vertices A, B, and C. The angle at vertex A measures 41.7 degrees. A ray of light enters the prism from the left side, bends due to refraction, and exits from the other side, following the law of refraction. 1. **Label A**: Apex of the prism with an angle of 41.7°. 2. **Label B and C**: The base vertices of the prism. 3. **Red Line**: Path of the light ray as it enters and exits the prism. 4. **Right Angle**: There is a right angle at vertex B. **Given Options:** - ⭘ 1.52 - ⭘ 1.54 - ⭘ 1.5 - ⭘ 1.49 By using Snell's Law and trigonometric calculations with the given angle: **Snell's Law:** \[ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \] Where: - \( \theta_1 \) and \( \theta_2 \) are the angles of incidence and refraction, respectively. - \( n_1 \) is the refractive index of the air (approximately 1). - \( n_2 \) is the refractive index of the glass. Using the apex angle and right-axis triangular relationship, the incident and refraction angles can also be calculated. Students may need additional steps to solve the problem precisely. Explore and choose the correct refractive index from the given options! For more detailed solution steps and understanding the principles, ensure to refer to your textbooks or educational resources.
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