Question

One technique for measuring the angle of a prism is shown in Figure P35.50. A parallel beam of light is directed on the angle so that parts of the beam reflect from opposite sides. Show that the angular separation of the two reflected beams is given by $B=2 A$. (FIGURE CANT COPY)

Name: Problem 50, Chapter 35: Physics for Scientists and Engineers
Uploaded: 2019-12-05T12:46:46-08:00
Duration: 3 min 28 s
Channel: Salamat Ali
Description: One technique for measuring the angle of a prism is shown in Figure P35.50. A parallel beam of light is directed on the angle so that parts of the beam reflect from opposite sides. Show that the angular separation of the two reflected beams is given by B=2 A. (FIGURE CANT COPY)

   One technique for measuring the angle of a prism is shown in Figure P35.50. A parallel beam of light is directed on the angle so that parts of the beam reflect from opposite sides. Show that the angular separation of the two reflected beams is given by $B=2 A$.
(FIGURE CANT COPY)

Physics for Scientists and Engineers

Raymond A. Serway,… 6th Edition

Chapter 35, Problem 50

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Solved by Expert Salamat Ali

12/05/2019

Step 1

We have a prism with an apex angle $ A $ and a parallel beam of light hitting the two faces of the prism at the apex. The light reflects off each face of the prism. We need to find the angular separation $ B $ between the two reflected beams. Show more…

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One technique for measuring the angle of a prism is shown in Figure P35.50. A parallel beam of light is directed on the angle so that parts of the beam reflect from opposite sides. Show that the angular separation of the two reflected beams is given by $B=2 A$. (FIGURE CANT COPY)

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Key Concepts

Reflection Geometry

By constructing normals and applying the law of reflection, one can analyze the geometric relationships between the incident and reflected beams. This approach helps in deriving relationships between the physical angles of reflecting surfaces and the angular separation of the beams.

Law of Reflection

When light strikes a surface, the angle of incidence is equal to the angle of reflection. This principle is fundamental in determining the path of light as it reflects off surfaces, ensuring that the angles at which light beams leave the surfaces mirror the angles at which they arrived.

Prism Geometry

A prism's apex angle determines how light interacts with its surfaces. When light is reflected from the two faces forming the prism’s angle, the overall angular deviation of the beams depends directly on this apex angle, leading to the result that the separation of the reflected beams is twice the prism angle.

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