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A light ray strikes a 10-cm-thick glass pane, making a 30° angle to the perpendicular to the glass as it enters.  When the ray reemerges into air on the other side of the pane, how much has it been displaced from where it would have been if the glass weren't there (this is the distance d indicated in the figure below)?

A light ray strikes a 10-cm-thick glass pane, making a 30° angle to the perpendicular to the glass as it enters.  When the ray reemerges into air on the other side of the pane, how much has it been displaced from where it would have been if the glass weren't there (this is the distance d indicated in the figure below)?

College Physics
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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A light ray strikes a 10-cm-thick glass pane, making a 30° angle to the perpendicular to the glass as it enters.  When the ray reemerges into air on the other side of the pane, how much has it been displaced from where it would have been if the glass weren't there (this is the distance d indicated in the figure below)?

A

1.25 cm
B

2.23 cm
C

1.94 cm
D

2.46 cm

 

### Refraction Through a Glass Slab **Diagram Explanation:** The diagram illustrates the path of a light ray as it travels from air into a glass slab and back into air. The glass slab is shown as a rectangular block with a thickness of \(10 \, \text{cm}\). **Key Elements:** 1. **Incident Ray:** The light ray traveling in the air before reaching the glass surface. 2. **Angle of Incidence (\(\theta_1\)):** The angle formed between the incident ray and the normal to the surface of the glass slab. In this diagram, \(\theta_1\) is \(30^\circ\). 3. **Refracted Ray:** The light ray inside the glass slab. Due to the change in medium from air to glass, the light ray bends towards the normal. 4. **Emergent Ray:** The light ray as it exits the glass slab back into the air. The light ray bends away from the normal upon passing from glass to air. 5. **Displacement (d):** This is the lateral shift of the ray as it passes through the glass slab and emerges on the other side. The displacement \(d\) is the question mark labeled in the diagram. **Concepts Involved:** - **Snell's Law:** Governs the angle of refraction, stating that \(\frac{\sin \theta_1}{\sin \theta_2} = \frac{n_2}{n_1}\), where \(n_2\) and \(n_1\) are the refractive indices of glass and air, respectively. - **Lateral Displacement:** Can be calculated based on the thickness of the slab, angle of incidence, and the refractive index of the glass. This setup is a classic example used to study the behavior of light as it refracts through different media, demonstrating key principles of optics such as refraction and lateral displacement.
Transcribed Image Text:### Refraction Through a Glass Slab **Diagram Explanation:** The diagram illustrates the path of a light ray as it travels from air into a glass slab and back into air. The glass slab is shown as a rectangular block with a thickness of \(10 \, \text{cm}\). **Key Elements:** 1. **Incident Ray:** The light ray traveling in the air before reaching the glass surface. 2. **Angle of Incidence (\(\theta_1\)):** The angle formed between the incident ray and the normal to the surface of the glass slab. In this diagram, \(\theta_1\) is \(30^\circ\). 3. **Refracted Ray:** The light ray inside the glass slab. Due to the change in medium from air to glass, the light ray bends towards the normal. 4. **Emergent Ray:** The light ray as it exits the glass slab back into the air. The light ray bends away from the normal upon passing from glass to air. 5. **Displacement (d):** This is the lateral shift of the ray as it passes through the glass slab and emerges on the other side. The displacement \(d\) is the question mark labeled in the diagram. **Concepts Involved:** - **Snell's Law:** Governs the angle of refraction, stating that \(\frac{\sin \theta_1}{\sin \theta_2} = \frac{n_2}{n_1}\), where \(n_2\) and \(n_1\) are the refractive indices of glass and air, respectively. - **Lateral Displacement:** Can be calculated based on the thickness of the slab, angle of incidence, and the refractive index of the glass. This setup is a classic example used to study the behavior of light as it refracts through different media, demonstrating key principles of optics such as refraction and lateral displacement.
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