Module No. 39
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1. A plane mirror forms a virtual image that is laterally inverted and the same size as the object. The image is located behind the mirror and an equal distance from the mirror as the object. 2. Spherical mirrors can be concave or convex. A concave mirror forms real or virtual images depending on the object position, while a convex mirror always forms a virtual, erect, and diminished image. 3. Key properties of mirrors include focal length, radius of curvature, and principal focus, which determine image characteristics. Concave mirrors are used for magnification while convex mirrors provide a wide field of view.
Module No. 39
- 1. 1 Module # 39 Mirrors Image Formed by a Plane Mirror The formation of image by a plane mirror is due to the fact that the rays traveling from an object to our eye change their direction after reflection so that they appear to come from points other than those from which they really started. The image of an object is observed in a direction in which the light enters our eye. Object Fig: Image formed by a plane mirror The image formed by a plane mirror can be located by the use of rectilinear propagation of light and geometrical methods. Let us consider the following diagram.
- 2. 2 Plane mirror Fig: Image of point object Light rays coming from a luminous object O are reflected by the plane mirror M and enter our eye. The line which joins the image I and the object O makes an angle of 90° with the surface of the mirror M. From the geometrical construction, the distance between the object and the mirror OM and the distance between the image and the mirror IM are equal. Therefore, we feel that the light rays come from the image I, but in fact they come from the object O and are reflected by the mirror. At the mirror surface, we find that the angle of incidence is equal to the angle of reflection. Characteristics of Image in case of Plane Mirror (1) Image is formed as far behind the mirror as the object is in front of it. (2) The image formed in a plane mirror is always virtual, i.e. it cannot be obtained on the screen.
- 3. 3 (3) The size of image is same as that of object, but, is laterally inverted, i.e., right side of the object appears as left and left side of the object appears as the right side of the image. Spherical Mirrors Mirrors whose surfaces are not plane but curved are called spherical mirrors as distinguished from plane mirrors. A spherical mirror is a silvered part or section of a hollow sphere. There are two types of spherical mirrors: 1 Concave mirror 2 Convex mirror Principal Focus of a Spherical Mirror The principal focus of a spherical mirror is that point on the principal axis to which all rays originally parallel and close to the principal axis converge, or from which they appear to diverge, after reflection from the mirror. Principal Axis of a Spherical Mirror The principal axis of a spherical mirror is the line joining the pole P or centre of the mirror to the centre of curvature C which is the centre of the sphere of which the mirror forms a part. OR
- 4. 4 It is the straight line passing through the centre of curvature and the pole. Focal Length of a Spherical Mirror The distance of principal focus from the pole of the spherical mirror is called focal length. Note: The focal length of concave mirror is taken as positive whereas the focal length of convex mirror is taken as negative. Sign Convention In the case of spherical mirrors, virtual as well as real images are formed which under certain conditions are diminished and under the other conditions are magnified. Therefore, it is necessary to define a sign convention so that we may be able to distinguish between real and virtual images as well magnified and diminished images. The sign convention is given as follows: (1) All distances are measured from the pole of the mirror. (2) Distances of real objects and images are taken as positive. (3) Distances of virtual objects and images and taken as negative.
- 5. 5 Aperture (of a Spherical Mirror) The diameter of the circular edge of a spherical mirror is known as aperture. Linear Magnification by a Spherical Mirror The magnification (m) by a spherical mirror is the ratio of the height of the image to the height of the object. Height of image Image distance from mirror Magnification (m) = ---------------------- = ---------------------------------------- Height of object Object distance from mirror Mirror Formula (Equation for Spherical Mirror) It is relation between the distances of the object and image from the pole of the mirror and the focal length of the mirror and is given as 1/f = 1/p + 1/q Where p = Distance of the object from the pole of the mirror. q = Distance of the image from the pole of the mirror, and f = focal length of the mirror
- 6. 6 Centre of Curvature The centre of the sphere, of which a concave or convex mirror is a part, is known as the centre of curvature of the spherical mirror. In other words, the centre of curvature (c) is the centre of the sphere from which a curved reflecting surface is obtained. Radius of Curvature The radius of curvature r is the distance between the pole P and the centre of curvature C of the spherical mirror. OR The distance between the pole of the spherical mirror and its centre of curvature is called radius of curvature. OR Radius of curvature is a straight line drawn from the centre of curvature to the reflecting curved surface. Note: In spherical mirrors, the radius of curvature is twice as large as its focal length. Concave Mirror The spherical mirror whose outer side is polished to reflect light from inner concave surface is called a concave mirror. Concave
- 7. 7 mirrors possess the ability to converge a parallel beam of light and are, therefore, called converging mirrors. Fig: Concave Mirror Uses of Concave Mirror (1) The image formed in the concave mirror is erect, magnified and virtual. Therefore, these mirrors are used as shaving mirrors because face is magnified and appears erect in them. (2) Doctors use ophthalmoscope which consist of concave mirrors for examination of ear, nose, throat and eye. (3) These are used as magnifiers. (4) Concave mirrors are used to throw light on the slides of the microscopes so that the slides can be viewed more clearly. (5) These are also used to focus light in case of search lights and head lights of automobiles. (6) Concave mirrors are used as objectives in the telescopes to concentrate a parallel beam of light from distant stars.
- 8. 8 Formation of Images in case of Concave Mirrors For image formation, we use two rays of light. It is observed that different images are formed when the object is placed at different positions. First Position If an object is placed in front of a concave mirror beyond its centre of curvature C, then, the image is formed between the principal focus F and the centre of curvature C. The image formed is real, inverted and diminished. Second Position If an object is placed in front of a concave mirror at the centre of curvature C, then, the image is also formed at the centre of curvature C. The image formed is real, inverted and equal in size of the object.
- 9. 9 Third Position If an object is placed in front of a concave mirror at a point between the centre of curvature C and the principal focus F, then, its image is formed beyond the centre of curvature C. The image formed is real, inverted and magnified. Fourth Position If an object is placed in front of a concave mirror at the principal focus F, then, its image is formed at infinity. The image formed is real, inverted and highly magnified. Fifth Position If an object is placed in front of a concave mirror between the principle focus F and the pole P, then, the image is formed
- 10. 10 somewhere behind the mirror. The image formed is virtual, erect end magnified. Formation of Virtual Image in a Concave Mirror Fig: Formation of image in a concave mirror If the object is placed in front of a concave mirror between principal focus F and pole P, the image is formed somewhere behind the mirror. This image is erect, virtual and magnified. Principal Focus (of a Concave Mirror) Rays of light parallel to the principal axis after reflection from a concave mirror converge to a point F on the principal axis. This point is known as principal focus of the concave mirror. Principal Focus (of a Convex Mirror) Rays of light parallel to the principal axis after reflection from a
- 11. 11 convex mirror appear to diverge from a point on the other side of the mirror. This point is known as principal focus of the convex mirror. Convex Mirror The spherical mirror whose inner concave side is polished to reflect light from outer convex surface is called a convex mirror. A convex mirror diverges a parallel beam of light incident on it. It is, therefore, known as a diverging mirror. Fig: Convex Mirror Uses of Convex Mirrors (1) Convex mirrors are used in automobiles to see the rear view because the field of view of these mirrors is large. (2) Convex mirrors can be used in telescopes as objectives.
- 12. 12 Formation of Image in Convex Mirrors For all distances of the object from the convex mirror, the image formed is always virtual, erect and diminished. Virtual image is formed behind the mirror between pole and the principal focus. Fig: Image formed by a convex mirror