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Refer to diagram 4. A prism is in the shape of an isosceles triangle, with base angle a = 52.4° is immersed in a liquid (index of refraction n= 1.54- not air!) A ray of light traveling in the liquid strikes the prism at angle of incidence e = 46.8°, and bends so it travels parallel to the base. Find the index of refraction of the material in the prism.

Refer to diagram 4. A prism is in the shape of an isosceles triangle, with base angle a = 52.4° is immersed in a liquid (index of refraction n= 1.54- not air!) A ray of light traveling in the liquid strikes the prism at angle of incidence e = 46.8°, and bends so it travels parallel to the base. Find the index of refraction of the material in the prism.

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**Problem Description:** A prism is in the shape of an isosceles triangle with a base angle of \( \alpha = 52.4^\circ \). This prism is immersed in a liquid with an index of refraction \( n = 1.54 \) (note: the liquid is not air). A ray of light traveling within the liquid strikes the prism at an angle of incidence \( \theta = 46.8^\circ \) and refracts so that it travels parallel to the base of the prism. Your task is to determine the index of refraction of the material composing the prism. **Diagram Explanation:** Although diagram 4 is referred to in the problem, the text provides key information to solve it: the shape of the prism is an isosceles triangle with given base angles, specific angles of incidence for the light rays, and indices of refraction for both the liquid and the prism material are needed. This scenario describes a situation involving Snell's Law and geometric optics principles to deduce the necessary optical properties.
Transcribed Image Text:**Problem Description:** A prism is in the shape of an isosceles triangle with a base angle of \( \alpha = 52.4^\circ \). This prism is immersed in a liquid with an index of refraction \( n = 1.54 \) (note: the liquid is not air). A ray of light traveling within the liquid strikes the prism at an angle of incidence \( \theta = 46.8^\circ \) and refracts so that it travels parallel to the base of the prism. Your task is to determine the index of refraction of the material composing the prism. **Diagram Explanation:** Although diagram 4 is referred to in the problem, the text provides key information to solve it: the shape of the prism is an isosceles triangle with given base angles, specific angles of incidence for the light rays, and indices of refraction for both the liquid and the prism material are needed. This scenario describes a situation involving Snell's Law and geometric optics principles to deduce the necessary optical properties.
**Diagram 4 Analysis** In this diagram, we see a triangular prism represented by a green triangle within a shaded rectangle. The interior of the triangle is filled with a slightly lighter shade of green, emphasizing its distinct shape. **Key Features:** 1. **Angles:** - Two angles are marked: α (alpha) and θ (theta). - Alpha (α) is positioned at the base of the triangle. - Theta (θ) is depicted as related to the angle of incidence, indicated by a dashed line intersecting the side of the triangle. 2. **Arrow:** - A black arrow enters the triangle from the left side, pointing towards the right. This arrow depicts a path, such as the direction of a light ray or vector, interacting with the triangle. 3. **Lines:** - A solid black line runs along the path of the arrow, while a dashed line indicates the trajectory of the angle θ. **Purpose and Interpretation:** This diagram can be used to demonstrate concepts in optics or geometry, such as the refraction of light through a prism, or vector forces acting at an angle. The markings suggest an interaction between the initial angle of approach (θ) and the resulting angle (α) within the prism environment, allowing for exploration of trigonometric or refractive properties.
Transcribed Image Text:**Diagram 4 Analysis** In this diagram, we see a triangular prism represented by a green triangle within a shaded rectangle. The interior of the triangle is filled with a slightly lighter shade of green, emphasizing its distinct shape. **Key Features:** 1. **Angles:** - Two angles are marked: α (alpha) and θ (theta). - Alpha (α) is positioned at the base of the triangle. - Theta (θ) is depicted as related to the angle of incidence, indicated by a dashed line intersecting the side of the triangle. 2. **Arrow:** - A black arrow enters the triangle from the left side, pointing towards the right. This arrow depicts a path, such as the direction of a light ray or vector, interacting with the triangle. 3. **Lines:** - A solid black line runs along the path of the arrow, while a dashed line indicates the trajectory of the angle θ. **Purpose and Interpretation:** This diagram can be used to demonstrate concepts in optics or geometry, such as the refraction of light through a prism, or vector forces acting at an angle. The markings suggest an interaction between the initial angle of approach (θ) and the resulting angle (α) within the prism environment, allowing for exploration of trigonometric or refractive properties.
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