4. Consider two plane mirrors located in the xz and yz planes. a) Locate the images of the arrow shown when viewed in this system of mirrors if the center of the arrow is at x = 2m, y = 1 m. EYE b) Sketch the image of the arrow at each of these locations. c) Prove that, in the case of rays which reach the eye after reflection in both mirrors, the ray as it leaves the arrow is travelling antiparallel to its direction when it reaches the eye.

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**Problem 4: Consider two plane mirrors located in the xz and yz planes.**

a) Locate the images of the arrow shown when viewed in this system of mirrors if the center of the arrow is at \( x = 2 \, \text{m}, y = 1 \, \text{m} \).

b) Sketch the image of the arrow at each of these locations.

c) Prove that, in the case of rays which reach the eye after reflection in both mirrors, the ray as it leaves the arrow is traveling antiparallel to its direction when it reaches the eye.

**Diagram Explanation:**

The diagram accompanying the text shows a two-dimensional coordinate system with axes labeled \( x \) and \( y \). The "eye" is indicated in the top left area of the graph. The position of the arrow is marked at coordinates (2, 1).

In this setup:
- The axis labeled \( y \) is vertical, 
- The axis labeled \( x \) is horizontal. 
- A small triangle near the top left represents the "eye" observing the scene.

This problem involves analyzing reflections in a system of two plane mirrors to determine how the position of an arrow changes when viewed in multiple reflections.
Transcribed Image Text:**Problem 4: Consider two plane mirrors located in the xz and yz planes.** a) Locate the images of the arrow shown when viewed in this system of mirrors if the center of the arrow is at \( x = 2 \, \text{m}, y = 1 \, \text{m} \). b) Sketch the image of the arrow at each of these locations. c) Prove that, in the case of rays which reach the eye after reflection in both mirrors, the ray as it leaves the arrow is traveling antiparallel to its direction when it reaches the eye. **Diagram Explanation:** The diagram accompanying the text shows a two-dimensional coordinate system with axes labeled \( x \) and \( y \). The "eye" is indicated in the top left area of the graph. The position of the arrow is marked at coordinates (2, 1). In this setup: - The axis labeled \( y \) is vertical, - The axis labeled \( x \) is horizontal. - A small triangle near the top left represents the "eye" observing the scene. This problem involves analyzing reflections in a system of two plane mirrors to determine how the position of an arrow changes when viewed in multiple reflections.
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