Science and Math: Physics

Mirrors

There are 3 types of mirror, the plane, concave, and convex mirror.

Plane Mirrors (also called flat mirrors)

An object viewed using a flat mirror appears to be located behind the mirror, because to the observer the diverging rays from the source appear to come from behind the mirror.

The images reflected in flat mirrors have the following properties:

The image distance q behind the mirror equals the object distance p from the mirror The image height h’ equals the object height h so that the lateral magnification. The image has an apparent left-right reversal The image is virtual, not real.

Real and Virtual Images Formed by Mirrors

The image, which can be obtained on the screen, are called real image. It is formed when the light rays after reflection or refraction actually, intersect each other. The image, which cannot be obtained on a screen, is called a virtual image. It is formed when the light rays after reflection or refraction do not actually intersect each other but they appear to diverge from it. Geometrically, they intersect when they are produced in the backward direction. Let us first discuss the image formed by the plane mirror.

Consider a plane mirror XY and an object placed at O. If a ray OA of light falls normally on the mirror, it goes back on the same path. Another ray OB is incident at any angle so that the reflected ray is BC. Here we observed that the reflected rays are not intersected by each other. So, produce both the reflected rays in the backward direction. They intersect at I. Therefore, I is the virtual image of the object at O. In the case of the concave mirror, the images formed by the mirror are real but in case if the object placed between focus and pole of the mirror, the image formed is virtual as shown in the diagrams.

Concave Mirror

When a parallel beam of light from a far off object falls on a concave mirror, a real, inverted point size image is formed at the focus of the concave mirror. We assume that the rays are paraxial, i.e. they are incident at points close to the pole of the mirror and make small angle with the principal axis. The reflected rays converge at a point F on the principal axis of the concave mirror. The reflected rays converges at a point F on the principal axis of a concave mirror.

One surface of the curved mirror is silvered. If the reflection takes place at the concave surface

The centre of the sphere is called the centre of curvature C.

The geometrical centre of the mirror is called its pole (P)

The line joining the pole of the mirror and its centre of curvature is called the principal axis.

When a parallel beam of light is incident on a spherical mirror, the point where the reflected ray converge on the principal axis is called the principal focus F.

Lets see the ray diagrams for concave mirror for the different positions of the object.

Ray Diagram Concave Mirror: Rules and some Examples

The images produced by spherical mirrors may be either real or virtual and may be either larger or smaller than the object. The image can be located graphically by adopting the following rules:

A ray parallel to the principal axis after reflection by a concave mirror passes through the principal focus of the concave mirror.

A ray passing through the centre of curvature retraces its path after reflection

A ray passing through the principal focus , after reflection is rendered parallel to the principal axis.

A ray striking the pole at an angle of incidencre i is reflected at the same angle i to the axis.

The ray diagram when the object is placed at the centre of curvature: We see that the object placed at the centre , the image is of same size, real and inverted and is at the centre.

The ray diagram when the object is placed after the centre of curvature.It is seen that the image is real , inverted , small in shape and lies between the centre C and focus F.

Not all people who are viewing the object in the mirror will sight along the same geometrical line of sight. The precise direction of the sight line depends on the location of the object, the location of the person, and the type of mirror. Yet all of the lines of sight, regardless of their direction, will pass through the image location. In fact, the image location is defined as the location where reflected rays intersect. Since all people see a reflected ray of light as they sight at an image in the mirror, then the image location must be the intersection point of these reflected rays.

Convex Mirror (also called spherical mirror)

A Convex mirror whose outer bulging out surface is the reflecting surface is called convex mirror. Convex mirror always forms a virtual image of a real object. When the rays of light after getting reflected from a mirror appear to meet at a point, a virtual image is formed. Virtual image can only be seen through a mirror but cannot be obtained on the screen. Virtual images are always erect with respect to the object. Convex mirrors used as rear view mirrors, in staircase on the double-deck buses, vigilance mirrors in big shops and in showrooms.

Rules to Draw the Ray Diagram for Convex Mirror

The following rays coming from an object are usually used to construct the ray diagrams for locating the images formed by a convex mirror.

1st: The diagram shows a ray of light traveling parallel the principal axis after reflection from a convex mirror appears to come from its focus behind the mirror.

2nd:A ray of light traveling towards the centre of curvature behind the mirror hits the mirror at 90° and is reflected back its own path. This is shown in the diagram given below.

A convex mirror gives only virtual image of real object irrespective of the position of the object. Here we describe the image formation by a convex mirror. The object is placed anywhere in front of the convex mirror. The ray parallel to the principal axis after reflection appears to come from the focus F behind the mirror. Another ray going towards the centre of curvature C behind the mirror gets reflected by the same path. The two reflected rays appear to intersect at a point between F and P behind the mirror. So, the image appears to be formed behind the mirror. So the image formed by the convex mirror is virtual, erect and smaller in size with respect to object.

Thus we see that for a convex mirror, the image formed is always virtual. Erect and smaller than the object whatever may be the position of the object in front of the mirror.

Lenses

A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element. A compound lens is an array of simple lenses (elements) with a common axis; the use of multiple elements allows more optical aberrations to be corrected than is possible with a single element. Lenses are typically made of glass or transparent plastic. Elements which refract electromagnetic radiation outside the visual spectrum are also called lenses: for instance, a microwave lens can be made from paraffin wax.

The variant spelling lense is sometimes seen. While it is listed as an alternative spelling in some dictionaries, most mainstream dictionaries do not list it as acceptable.

Convex Lens (also called Converging Lens)

When these parallel rays pass through a Convex lens, they converge on a point and then diverge as they go on their way. This point, through which the rays all pass, is called the focal point F. Since we can turn the lens around and it behaves the same way, there is a focal point on both sides of the lens. The distance from the lens to the focal point is called the focal length and is labeled f. The focal length is positive for a convex lens.

The following points are to be kept in mind while drawing ray diagrams for convex lens:-

A ray of light passing through the optical center of a convex lens passes through the lens undeviated.
A ray of light parallel to the principal axis, on passing through the lens, gets deviated and passes through the focal point of the lens on the other side.
A ray of light passing through the focus of a convex, on passing through the lens, gets deviated such that it travels parallel to the principal axis on the other side.

Ray Diagrams for Convex Lenses for Different Positions of the Object:

When an object is placed at different positions with respect to the focal length, the double focal length, etc of the a convex lens, images formed of that object exhibit different characteristics according to its relative position to the lens. The location and characteristics of images formed in different scenarios can be predetermined by the help of which appropriate convex lenses are used in the correct positions in devices.

Object at Infinity Object Beyond 2F

Object at 2F Object between F and 2 F

ray diagram when object is between F and 2F

Object at F

Object Between F and O

Position of object	Position of image	Nature of image
Object at infinity	Image at focus	Real, inverted, small in size
Object beyond 2F	Image formed between F and 2F	Real, inverted, smaller in size
Object at 2F	Image is also at 2F	Real, inverted, same size
Object between F and 2F	Image beyond 2F	Real, inverted, large in size
Object at F	Image at infinity	Highly magnified
Object between F and O	Image on the same side of the object	Virtual, erect, magnified.

Concave Lens (also called Diverging Lens)

When these parallel rays pass through a diverging lens, they diverge from a point on the other side of the lens. This point is called the focal point F. Since we can turn the lens around and it behaves the same way, there is a focal point on both sides of the lens. The distance from the lens to the focal point is called the focal length and is labeled f. The focal length is negative for a diverging lens.

The following rays are considered while constructing ray diagrams for locating the images formed by a concave lens for the various position of the object.