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# Ray Diagrams – Introduction, Question and Answers

May 11, 2023

## Introduction to Ray Diagrams

### Introduction:

Spherical mirrors form various kinds of images, such as real, virtual, inverted, upright, diminished, magnified, etc. The characteristics of the image depend upon the position of the object w.r.t the mirror. This can be seen by drawing the ray diagrams. In this section, we will be looking at the various basic concepts that one requires to bear in mind before attempting to draw the ray diagrams for various positions of the object in front of a spherical mirror.

### Explanation:

Consider an extended object of finite size placed in front of a spherical mirror. An arrow usually denotes it. An infinite number of light rays originate from each small portion of this object. However, it would be convenient to choose either 2 or 3 of the rays to make the ray diagram clear. For each ray incident on the mirror, the corresponding reflected ray needs to be drawn in order to locate the image.

### Drawing the Reflected Ray:

To draw a reflected ray for a particular incident ray for the spherical mirrors,

1. The normal line should be drawn at the point of incidence.
2. The angle of incidence should be measured.
3. An angle equal to the angle of incidence should be constructed on the normal line to get the reflected ray.

The normal line at a particular point is perpendicular to the surface of the mirror at that point.

The normal line at a point of a concave mirror can be drawn by simply joining its center of curvature to the point. The normal line at a point of a convex mirror can be drawn by extending the line joining the point and its center of curvature in front of the reflecting surface.

The reflected ray for a particular incident ray for spherical mirrors can be drawn by using the laws of reflection, i.e.,

∠I = ∠r

### Predictable Reflected Rays:

However, the above process of drawing reflected rays is quite cumbersome. Therefore, the rays for which the reflected rays are predictable are chosen for the sake of ease of drawing the ray diagrams. The image of a point on the extended object is formed at the point of intersection of at least 2 reflected rays corresponding to the incident rays originating from that point.

A ray parallel to the principal axis,

• Passes through the principal focus after reflection in case of a concave mirror.
• It appears to diverge from the principal focus after reflection in the case of a convex mirror.
• An incident ray passing through the principal focus of a concave mirror goes parallel to the principal axis after reflection.
• An incident ray heading towards the principal focus of a convex mirror goes parallel to the principal axis after reflection.
• An incident ray passing through the center of curvature of a concave mirror goes along the same path after reflection.
• An incident ray heading towards the center of curvature of a convex mirror goes along the same path after reflection.

This is because the incident rays go along the normal to the reflecting surface in this case.

1. Draw the corresponding normal lines and reflected rays of the incident rays shown in the diagrams below.

2. Draw the corresponding normal lines and reflected rays of the incident rays shown in the diagrams below.

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