Definition 1: Image

An image is a representation of an object formed by a mirror or lens. Light from the image is seen.

Figure 1: An object formed in a mirror is real and upright.

If you place a candle in front of a mirror, you now see two candles. The actual, physical candle is called the object and the picture you see in the mirror is called the image. The object is the source of the incident rays. The image is the picture that is formed by the reflected rays.

The object could be an actual source that emits light, such as a light bulb or a candle. More commonly, the object reflects light from another source. When you look at your face in the mirror, your face does not emit light. Instead, light from a light bulb or from the sun reflects off your face and then hits the mirror. However, in working with light rays, it is easiest to pretend the light is coming from the object.

An image formed by reflection may be real or virtual. A real image occurs when light rays actually intersect at the image. A real image is inverted, or upside down. A virtual image occurs when light rays do not actually meet at the image. Instead, you "see" the image because your eye projects light rays backward. You are fooled into seeing an image! A virtual image is erect, or right side up (upright).

You can tell the two types apart by putting a screen at the location of the image. A real image can be formed on the screen because the light rays actually meet there. A virtual image cannot be seen on a screen, since it is not really there.

To describe objects and images, we need to know their locations and their sizes. The distance from the mirror to the object is the object distance, dodo.

The distance from the mirror to the image is the image distance, didi.

Investigation : Image formed by a mirror

1. Stand one step away from a large mirror
2. What do you observe in the mirror? This is called your image.
3. What size is your image? Bigger, smaller or the same size as you?
4. How far is your image from you? How far is your image from the mirror?
5. Is your image upright or upside down?
6. Take one step backwards. What does your image do? How far are you away from your image?
7. If it were a real object, which foot would the image of you right show fit?

Figure 2: An image in a mirror is virtual, upright, the same size and inverted front to back.

When you look into a mirror, you see an image of yourself.

The image created in the mirror has the following properties:

Virtual images are images formed in places where light does not really reach. Light does not really pass through the mirror to create the image; it only appears to an observer as though the light were coming from behind the mirror. Whenever a mirror creates an image which is virtual, the image will always be located behind the mirror where light does not really pass.

Definition 2: Virtual Image

A virtual image is upright, on the opposite side of the mirror as the object, and light does not actually reach it.

We draw ray diagrams to predict the image that is formed by a plane mirror. A ray diagram is a geometrical picture that is used for analyzing the images formed by mirrors and lenses. We draw a few characteristic rays from the object to the mirror. We then follow ray-tracing rules to find the path of the rays and locate the image.

The ray diagram for the image formed by a plane mirror is the simplest possible ray diagram. (Reference) shows an object placed in front of a plane mirror. It is convenient to have a central line that runs perpendicular to the mirror. This imaginary line is called the principal axis.

Method: Ray Diagrams for Plane Mirrors

Ray diagrams are used to find the position and size and whether the image is real or virtual.

Figure 8

Suppose a light ray leaves the top of the object traveling parallel to the principal axis. The ray will hit the mirror at an angle of incidence of 0 degrees. We say that the ray hits the mirror normally. According to the law of reflection, the ray will be reflected at 0 degrees. The ray then bounces back in the same direction. We also project the ray back behind the mirror because this is what your eye does.

Another light ray leaves the top of the object and hits the mirror at its centre. This ray will be reflected at the same angle as its angle of incidence, as shown. If we project the ray backward behind the mirror, it will eventually cross the projection of the first ray we drew. We have found the location of the image! It is a virtual image since it appears in an area that light cannot actually reach (behind the mirror). You can see from the diagram that the image is erect and is the same size as the object. This is exactly as we expected.

We use a dashed line to indicate that the image is virtual.

The second class of mirrors that we will look at are spherical mirrors. These mirrors are called spherical mirrors because if you take a sphere and cut it as shown in Figure 10 and then polish the inside of one and the outside of the other, you will get a concave mirror and convex mirror as shown. These two mirrors will be studied in detail.

The centre of curvature is the point at the centre of the sphere and describes how big the sphere is.

Figure 10: When a sphere is cut and then polished to a reflective surface on the inside a concave mirror is obtained. When the outside is polished to a reflective surface, a convex mirror is obtained.

The first type of curved mirror we will study are concave mirrors. Concave mirrors have the shape shown in Figure 11. As with a plane mirror, the principal axis is a line that is perpendicular to the centre of the mirror.

Figure 11: Concave mirror with principal axis.

If you think of light reflecting off a concave mirror, you will immediately see that things will look very different compared to a plane mirror. The easiest way to understand what will happen is to draw a ray diagram and work out where the images will form. Once we have done that it is easy to see what properties the image has.

First we need to define a very important characteristic of the mirror. We have seen that the centre of curvature is the centre of the sphere from which the mirror is cut. We then define that a distance that is half-way between the centre of curvature and the mirror on the principal axis. This point is known as the focal point and the distance from the focal point to the mirror is known as the focal length (symbol ff). Since the focal point is the midpoint of the line segment joining the vertex and the center of curvature, the focal length would be one-half the radius of curvature. This fact can come in very handy, remember if you know one then you know the other!

Definition 3: Focal Point

The focal point of a mirror is the midpoint of a line segment joining the vertex and the centre of curvature. It is the position at which all parallel rays are focussed.

Why are we making such a big deal about this point we call the focal point? It has an important property we will use often. A ray parallel to the principal axis hitting the mirror will always be reflected through the focal point. The focal point is the position at which all parallel rays are focussed.

Figure 12: All light rays pass through the focal point.

Figure 13: A concave mirror with three rays drawn to locate the image. Each incident ray is reflected according to the Law of Reflection. The intersection of the reflected rays gives the location of the image. Here the image is real and inverted.

From Figure 13, we see that the image created by a concave mirror is real and inverted, as compared to the virtual and erect image created by a plane mirror.

Definition 4: Real Image

A real image can be cast on a screen; it is inverted, and on the same side of the mirror as the object.

The second type of curved mirror we will study are convex mirrors. Convex mirrors have the shape shown in Figure 14. As with a plane mirror, the principal axis is a line that is perpendicular to the centre of the mirror.

We have defined the focal point as that point that is half-way along the principal axis between the centre of curvature and the mirror. Now for a convex mirror, this point is behind the mirror. A convex mirror has a negative focal length because the focal point is behind the mirror.

Figure 14: Convex mirror with principle axis, focal point (F) and centre of curvature (C). The centre of the mirror is the optical centre (O).

To determine what the image from a convex mirror looks like and where the image is located, we need to remember that a mirror obeys the laws of reflection and that light appears to come from the image. The image created by a convex mirror is shown in Figure 15.

Figure 15: A convex mirror with three rays drawn to locate the image. Each incident ray is reflected according to the Law of Reflection. The reflected rays diverge. If the reflected rays are extended behind the mirror, then their intersection gives the location of the image behind the mirror. For a convex mirror, the image is virtual and upright.

From Figure 15, we see that the image created by a convex mirror is virtual and upright, as compared to the real and inverted image created by a concave mirror.

The properties of mirrors are summarised in Table 1.

In Figure 13 and Figure 15, the height of the object and image arrows were different. In any optical system where images are formed from objects, the ratio of the image height, hihi, to the object height, hoho is known as the magnification, mm.

This is true for the mirror examples we showed above and will also be true for lenses, which will be introduced in the next sections. For a plane mirror, the height of the image is the same as the height of the object, so the magnification is simply m=hiho=1m=hiho=1. If the magnification is greater than 1, the image is larger than the object and is said to be magnified. If the magnification is less than 1, the image is smaller than the object so the image is said to be diminished.