Spherical Mirrors, Concave Mirrors, Convex Mirrors, Magnification, Physics 10 1/ Spherical Mirrors 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 7.16 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. 2/ Concave Mirrors The first type of curved mirror we will study are concave mirrors. Concave mirrors have the shape shown in Figure 7.17. As with a plane mirror, the principal axis is a line that is perpendicular to the centre of the mirror. 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 Figure 7.16: 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. 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 f ). 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: 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 7.19: 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 7.19, 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: 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. Convex Mirrors The second type of curved mirror we will study are convex mirrors. Convex mirrors have the shape shown in Figure 7.20. 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 7.20: 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 7.21. Figure 7.21: 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 7.21, 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. 3/ Magnification In Figures 7.19 and 7.21, 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, h$_{i}$, to the object height, ho is known as the magnification, m. \[m = \dfrac{h_i}{h_o}\]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 \[m = \dfrac{h_i}{h_o}\] = 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. Worked Example : Magnification Question: A concave mirror forms an image that is 4,8 cm high. The height of the object is 1,6 cm. Calculate the magnification of the mirror. Answer Step 1 : Identify what is given and what is asked. Image height h$_{i}$ = 4,8 cm Object height ho = 1,6 cm Magnification m = ? Step 2 : Substitute the values and calculate m. \[m = \dfrac{h_i}{h_o}\] = 3 The magnification is 3 times. Xem thêm: Physics 10.VI Geometrical Optics High School Students Studying the Sciences Physics