Chapter 4: Problem 57

What are the three rays we consider to draw ray diagrams in order to show the formation of images by spherical mirrors? How do they propagate after reflection?

Short Answer

Expert verified

Answer: The three main rays involved in image formation using spherical mirrors are the parallel-ray, center-ray, and focal-ray. After reflecting off the mirror, the parallel-ray passes through the focal point, the center-ray follows its initial path, and the focal-ray becomes parallel to the principal axis.

Step by step solution

Identifying the Three Rays

The three rays that we consider to draw ray diagrams for spherical mirrors are: 1. The "parallel-ray": A light ray that is parallel to the principal axis (the horizontal line passing through the center of the mirror). 2. The "center-ray": A light ray that passes through the center of the curvature of the mirror (the center of the sphere from which the mirror is a part). 3. The "focal-ray": A light ray that passes through the focal point of the mirror (the point halfway between the center of the curvature and the mirror's vertex).

Reflection of the Parallel-Ray

When the parallel-ray reflects off the spherical mirror, it passes through the focal point. In the case of a concave mirror, the reflection causes the ray to converge towards the principal axis, while for convex mirrors, it diverges away from the principal axis.

Reflection of the Center-Ray

The center-ray, after reflecting off the spherical mirror, follows the same path as it did before reflecting. This occurs because the center-ray hits the mirror perpendicularly, following the normal line of the mirror's surface at the point of incidence. Therefore, the angle of incidence is 0 degrees, and the angle of reflection is also 0 degrees.

Reflection of the Focal-Ray

When the focal-ray reflects off the spherical mirror, it becomes parallel to the principal axis. For a concave mirror, this means the reflected focal-ray will converge with the other rays after reflection, while for a convex mirror, it will diverge away from the other rays. This is due to the shape and orientation of the mirror's surface. In conclusion, to draw a ray diagram for the formation of images by spherical mirrors, we must consider the three main rays: the parallel-ray, center-ray, and focal-ray. After reflecting off the mirror, the parallel-ray passes through the focal point, the center-ray follows its initial path, and the focal-ray becomes parallel to the principal axis.

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What are the three rays we consider to draw ray diagrams in order to show the formation of images by spherical mirrors? How do they propagate after reflection?

Short Answer

Step by step solution

Identifying the Three Rays

Reflection of the Parallel-Ray

Reflection of the Center-Ray

Reflection of the Focal-Ray

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