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A ray of light traveling in medium 1 (index of refraction n1 = 1.55, not air!) strikes the side of a prism along the normal. The prism is an isosceles triangle with base angle a = 32.7° and index of refraction n2 = 1.11. The ray passes through the prism and exits at point A (back into medium 1). It then strikes a plane mirror (parallel to the bottom of the prism and distance d = 20.5 cm away), reflects, and enters the prism again at point B. Find x, the distance between points A and B, in cm.

A ray of light traveling in medium 1 (index of refraction n1 = 1.55, not air!) strikes the side of a prism along the normal. The prism is an isosceles triangle with base angle a = 32.7° and index of refraction n2 = 1.11. The ray passes through the prism and exits at point A (back into medium 1). It then strikes a plane mirror (parallel to the bottom of the prism and distance d = 20.5 cm away), reflects, and enters the prism again at point B. Find x, the distance between points A and B, in cm.

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Refer to diagram 2. A ray of light traveling in medium 1 (index of refraction \( n_1 = 1.55, \text{not air!} \)) strikes the side of a prism along the normal. The prism is an isosceles triangle with base angle \( \alpha = 32.7^\circ \) and index of refraction \( n_2 = 1.11 \). The ray passes through the prism and exits at point A (back into medium 1). It then strikes a plane mirror (parallel to the bottom of the prism and distance \( d = 20.5 \) cm away), reflects, and enters the prism again at point B. Find \( x \), the distance between points A and B, in cm.
Transcribed Image Text:Refer to diagram 2. A ray of light traveling in medium 1 (index of refraction \( n_1 = 1.55, \text{not air!} \)) strikes the side of a prism along the normal. The prism is an isosceles triangle with base angle \( \alpha = 32.7^\circ \) and index of refraction \( n_2 = 1.11 \). The ray passes through the prism and exits at point A (back into medium 1). It then strikes a plane mirror (parallel to the bottom of the prism and distance \( d = 20.5 \) cm away), reflects, and enters the prism again at point B. Find \( x \), the distance between points A and B, in cm.
**Diagram 2 Explanation** This diagram illustrates the refraction of light through a prism. It features a triangular prism with two refracting surfaces and a horizontal base. - **Prism Composition**: The prism has two regions with different refractive indices, labeled \(n_1\) and \(n_2\). - **Incident and Refracted Rays**: - **Incident Ray**: An incoming light ray approaches the first surface of the prism at point **A** with an angle of incidence \( \alpha \). - **Refracted Rays**: This ray refracts at point **A** into the prism, changing direction due to the difference in refractive indices. The ray then travels through the prism and exits at point **B**, refracting again as it moves from the material with refractive index \(n_2\) to air. - **Path of Light**: - The light enters the prism at **A**, travels to an internal point **x**, and exits at **B**. - The vertical distance from the point **B** to the horizontal line is marked as \(d\). - **Angles and Labels**: - The angle of incidence at the first surface is labeled \( \alpha \). - Points **A**, **x**, and **B** denote successive positions of light as it passes through the prism. This setup demonstrates the basic principles of refraction, showing how light rays bend when entering and exiting materials with different optical densities.
Transcribed Image Text:**Diagram 2 Explanation** This diagram illustrates the refraction of light through a prism. It features a triangular prism with two refracting surfaces and a horizontal base. - **Prism Composition**: The prism has two regions with different refractive indices, labeled \(n_1\) and \(n_2\). - **Incident and Refracted Rays**: - **Incident Ray**: An incoming light ray approaches the first surface of the prism at point **A** with an angle of incidence \( \alpha \). - **Refracted Rays**: This ray refracts at point **A** into the prism, changing direction due to the difference in refractive indices. The ray then travels through the prism and exits at point **B**, refracting again as it moves from the material with refractive index \(n_2\) to air. - **Path of Light**: - The light enters the prism at **A**, travels to an internal point **x**, and exits at **B**. - The vertical distance from the point **B** to the horizontal line is marked as \(d\). - **Angles and Labels**: - The angle of incidence at the first surface is labeled \( \alpha \). - Points **A**, **x**, and **B** denote successive positions of light as it passes through the prism. This setup demonstrates the basic principles of refraction, showing how light rays bend when entering and exiting materials with different optical densities.
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