Image Formation By Spherical Mirrors

Image Formation By Spherical Mirrors  

Introduction

By using the concept of predictable reflected rays, it becomes convenient to locate images formed by the spherical mirrors at various positions of an object. Both the laws of reflection are obeyed in all the ray diagrams, i.e., the angle of incidence is always equal to the angle of reflection. The image of an object placed at a particular position in front of a spherical mirror can be located by using the incident rays with predictable reflected rays. 

Explanation

Image formation by a concave mirror: 

Object at infinity: 

The light rays approaching the mirror from an object located at an infinitely large distance from it appear to be parallel to each other. These parallel light rays after reflection from the concave mirror pass through the focus. 

The image is, 

1. Formed at focus, 

2. Point sized 

3. Real and inverted 

Object located behind the center of curvature: 

Two rays are chosen to arise from the head of the extended object. 

1. The first one is parallel to the principal axis, which passes through the focus after reflection. 

2. The second is through the center of curvature, which goes along the same path after reflection. 

The image is, 

1. Formed between the center of curvature and the focus, 

2. Diminished  

3. Real and inverted 

Object at center of curvature: 

Two rays are chosen to arise from the head of the extended object. 

1. The first one is parallel to the principal axis, which passes through the focus after reflection. 

2. The second is through the focus, which goes parallel to the principal axis after reflection. 

The image is, 

1. Formed at the center of curvature 

2. Same size as the object  

3. Real and inverted 

Object located between the center of curvature and the focus: 

Two rays are chosen to arise from the head of the extended object. 

1. The first one is parallel to the principal axis, which passes through the focus after reflection. 

2. The second incidents on the mirror as if it is arising from the center of curvature. It passes through C after reflection. 

The image is, 

1. Formed beyond the center of curvature 

2. Magnified 

3. Real and inverted 

Object located at focus: 

Two rays are chosen to arise from the head of the extended object. 

1. The first one is parallel to the principal axis, which passes through the focus after reflection. 

2. The second incidents on the mirror as if it is arising from the center of curvature. It passes through C after reflection. 

The two reflected rays turn out to be parallel to each other, which are said to meet at infinity. 

The image is, 

1. Formed at infinity 

2. Highly magnified 

3. Real and inverted 

Object located between the focus and the pole: 

Two rays are chosen to arise from the head of the extended object. 

1. The first one incidents obliquely on the pole and reflects obliquely. Here the principal axis is the normal line. 

2. The second incidents on the mirror as if it is arising from the center of curvature. It passes through C after reflection. 

The two reflected rays turn out to be parallel to diverge from a point behind the mirror, where the image of the object is formed. 

The image is, 

1. Formed behind the mirror, 

2. Magnified, 

3. Virtual and upright. 

Uses of concave mirrors: 

When the object lies in between the pole and the focus of a concave mirror, it forms a virtual, upright and magnified image of the object.  

This property of concave mirrors is used in:

1. Shaving mirrors 

2. Makeup mirrors 

3. Dental mirrors. 

As all the above mirrors are required to produce a magnified image of the person in front of it, concave mirrors are used. 

A concave mirror can also direct the light from a source (spreading in all directions) in one direction by reflecting it, especially when the source of light lies at the focus of the mirror. This generates a parallel beam of light.  

Because of this property, concave mirrors are used in  

1. Headlights of vehicles 

2. Torches 

Image formation by convex mirrors: 

Object at infinity: 

The light rays approaching the mirror from an object located at an infinitely large distance from it appear to be parallel to each other. 

These parallel light rays after reflection from the convex mirror appear to diverge from the focus. 

The image is, 

1. Formed at focus, 

2. Point sized, 

3. Virtual and upright. 

Object located at a finite distance from the mirror: 

Two rays are chosen to arise from the head of the extended object. 

1. The first one incidents parallel to the principal axis and appears to diverge from the focus after reflection. 

2. The second incidents on the mirror as if it is approaching the center of curvature. It goes along the same path after reflection. 

The reflected rays seem to diverge from a point behind the mirror, where the image of the object is formed.  

The image is, 

1. Formed between pole and focus 

2. Diminished 

3. Virtual and upright 

Uses of convex mirrors: 

A convex mirror covers a wide area in the image it forms. Because of this property, it is used as, 

1. Rear-view mirror in the vehicles to see the vehicles approaching from the back 

2. Shop security mirror to watch the activities of the customers 

3. Road safety mirror at turns on the roads, for a driver to watch the vehicles approaching from the other side. 

Summary