Mirrors, Image Formation, Physics 10, Geometrical Optics 1/ Mirrors A mirror is a highly reflective surface. The most common mirrors are flat and are known as plane mirrors. Household mirrors are plane mirrors. They are made of a flat piece of glass with a thin layer of silver nitrate or aluminium on the back. However, other mirrors are curved and are either convex mirrors or are concave mirrors. The reflecting properties of all three types of mirrors will be discussed in this section. 2/ Image Formation Definition: Image An image is a representation of an object formed by a mirror or lens. Light from the image is seen. 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. Figure 7.13: An object formed in a mirror is real and upright. 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, do. The distance from the mirror to the image is the image distance, di. 3/ Plane Mirrors Activity :: 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. Lift your left arm. Which arm does your image lift? When you look into a mirror, you see an image of yourself. The image created in the mirror has the following properties: 1. The image is virtual. Figure 7.14: An image in a mirror is virtual, upright, the same size and laterally inverted. 2. The image is the same distance behind the mirror as the object is in front of the mirror. 3. The image is laterally inverted. This means that the image is inverted from side to side. 4. The image is the same size as the object. 5. The image is upright. 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: Virtual Image A virtual image is upright, on the opposite side of the mirror as the object, and light does not actually reach it. 4/ Ray Diagrams 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. Important: A mirror obeys the Law of Reflection. The ray diagram for the image formed by a plane mirror is the simplest possible ray diagram. Figure 7.15 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. Important: Ray diagrams The following should be remembered when drawing ray diagrams: 1. Objects are represented by arrows. The length of the arrow represents the height of the object. 2. If the arrow points upwards, then the object is described as upright or erect. If the arrow points downwards then the object is described as inverted. 3. If the object is real, then the arrow is drawn with a solid line. If the object is virtual, then the arrow is drawn with a dashed line. Method: Ray Diagrams for Plane Mirrors Ray diagrams are used to find the position and size and whether the image is real or virtual. 1. Draw the plane mirror as a straight line on a principal axis. 2. Draw the object as an arrow in front of the mirror. 3. Draw the image of the object, by using the principle that the image is placed at the same distance behind the mirror that the object is in front of the mirror. The image size is also the same as the object size. 4. Place a dot at the point the eye is located. 5. Pick one point on the image and draw the reflected ray that travels to the eye as it sees this point. Remember to add an arrowhead. 6. Draw the incident ray for light traveling from the corresponding point on the object to the mirror, such that the law of reflection is obeyed. 7. Continue for other extreme points on the object. Figure 7.15: Ray diagram to predict the image formed by a plane mirror. 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.