Concave and Convex Mirror
Concave and Convex Mirror The reflecting surface of a spherical mirror may be curved inwards or outwards. A spherical mirror, whose reflecting surface is curved inwards, that is, faces towards the center of the sphere, is called a concave mirror. A spherical mirror whose reflecting surface is curved outwards is called a convex mirror. The schematic representation of these mirrors is shown in Fig. 10.1.
Figure 10.1
Schematic representation of spherical mirrors; the shaded side is non-reflecting.
You may note in these diagrams that the back of the mirror is shaded.
You may now understand that the surface of the spoon curved inwards can be approximated to a concave mirror and the surface of the spoon bulged outwards can be approximated to a convex mirror.
Before we move further on spherical mirrors, we need to recognize and understand the meaning of a few terms. These terms are commonly used in discussions about spherical mirrors. The center of the reflecting surface of a spherical mirror is a point called the pole. It lies on the surface of the mirror. The pole is usually represented by the letter P.
The reflecting surface of a spherical mirror forms a part of a sphere. This sphere has a centre. This point is called the centre of curvature of the spherical mirror. It is represented by the letter C. Please note that the centre of curvature is not a part of the mirror. It lies outside its reflecting surface. The centre of curvature of a concave mirror lies in front of it. However, it lies behind the mirror in case of a convex mirror. You may note this in Fig.10.2 (a) and (b).
The radius of the sphere of which the reflecting surface of a spherical mirror forms a part, is called the radius of curvature of the mirror. It is represented by the letter R. You may note that the distance PC is equal to the radius of curvature. Imagine a straight line passing through the pole and the centre of curvature of a spherical mirror. This line is called the principal axis. Remember that principal axis is normal to the mirror at its pole. Let us understand an important term related to mirrors, through an Activity.
Activity 10.2
CAUTION: Do not look at the Sun directly or even into a mirror reflecting sunlight. It may damage your eyes.
Hold a concave mirror in your hand and direct its reflecting surface towards the Sun.
Direct the light reflected by the mirror onto a sheet of paper held close to the mirror.
Move the sheet of paper back and forth gradually until you find on the paper sheet a bright, sharp spot of light.
Hold the mirror and the paper in the same position for a few minutes. What do you observe? Why?
The paper at first begins to burn producing smoke. Eventually, it may even catch fire. Why does it burn? The light from the Sun is converged at a point, as a sharp, bright spot by the mirror. In fact, this spot of light is the image of the Sun on the sheet of paper. This point is the focus of the concave mirror. The heat produced due to the concentration of sunlight ignites the paper. The distance of this image from the position of the mirror gives the approximate value of the focal length of the mirror.
Let us try to understand this observation with the help of a ray diagram.
Observe Fig.10.2 (a) closely.
A number of rays parallel to the principal axis are falling on a concave mirror. Observe the reflected rays. They are all meeting/intersecting at a point on the principal axis of the mirror. This point is called the principal focus of the concave mirror.
Similarly, observe Fig. 10.2 (b).
How are the rays parallel to the principal axis, reflected by a convex mirror? The reflected rays appear to come from a point on the principal axis. This point is called the principal focus of the convex mirror. The principal focus is represented by the letter F. The distance between the pole and the principal focus of a spherical mirror is called the focal length. It is represented by the letter f.
The reflecting surface of a spherical mirror is by-and-large spherical. The surface, then, has a circular outline. The diameter of the reflecting surface of a spherical mirror is called its aperture. In Fig.10.2, distance MN represents the aperture. We shall consider in our discussion only such spherical mirrors whose aperture is much smaller than its radius of curvature.
Is there a relationship between the radius of curvature R, and focal length f, of a spherical mirror? For spherical mirrors of small apertures, the radius of curvature is found to be equal to twice the focal length. We put this as R = 2f. This implies that the principal focus of a spherical mirror lies midway between the pole and centre of curvature.
Image Formation by Spherical Mirrors
You have studied the image formation by plane mirrors. You also know the nature, position, and relative size of the images formed by them. How about the images formed by spherical mirrors? How can we locate the image formed by a concave mirror for different positions of the object? Are the images real or virtual? Are they enlarged, diminished, or have the same size? We shall explore this with an Activity.
Activity 10.3
You have already learnt a way of determining the focal length of a concave mirror. In Activity 10.2, you have seen that the sharp bright spot of light you got on the paper is, in fact, the image of the Sun. It was a tiny, real, inverted image. You got the approximate focal length of the concave mirror by measuring the distance of the image from the mirror.
You will see in the above Activity that the nature, position, and size of the image formed by a concave mirror depend on the position of the object in relation to points P, F, and C. The image formed is real for some positions of the object. It is found to be a virtual image for a certain other position. The image is either magnified, reduced, or has the same size, depending on the position of the object. A summary of these observations is given for your reference in Table 10.1.
Table 10.1 Image formation by a concave mirror for different positions of the object