Earlier still or dark water collected in a vessel was considered or used as mirrors by ancient people. Then as days passed obsidian mirrors came in to existence followed by metal coated glass mirrors this led to discovery of metal coated spherical or parabolic mirrors. A spherical mirror is a mirror which has the shape of a piece cut out of a spherical surface. There are two types of spherical mirrors: concave, and convex. These mirrors are also known as parabolic mirrors discovered in mid9th century Ibn al haytham and Ibn sahl.parabolic mirrors were described in classical antiquity written by mathematicianDiocles . In addition to these researches Ptolemy also carried out experiments with curved polished iron mirrors and discussed about convex spherical and concave spherical mirrors in his book optics. Inspite of these researches finding the focal length of spherical mirror was a though task but finally Ibn al Hay tham got a break through by finding out the focal length of curved surfaces using the laws of reflection.he stated that “All the reflected rays of a mirror converge or diverge and meet at a point known as focus and the distance between focus and pole of mirror is known as focal point of mirror.’’Also many scientists came to a conclusion that spherical mirrors can be divided into concave and convex mirrors. Spheri cal mirrors Concave mirrors Convex mirrors The invention of concave and convex mirrors led to many chan ges and have become a part of ou r life . Mirrors are the basic means of viewing our own beauty. Generally we can classify the mirrors into the following two types as i. Plane mirrors ii. Curved mirrors. Generally mirrors refer to plane mirrors. But if the surface of a mirror is curved it is said to be a curved mirror. If the curved mirror is a part of a huge sphere, then the mirror is a spherical mirror. Terms Associated with Spherical Mirrors Centre of curvature (C) is the centre of the sphere, of which the mirror is a part. Radius of curvature (R) is the radius of the sphere, of which the mirror is a part. Pole (P) is the geometric centre of the spherical mirror. Principal axis is the line joining the pole and the centre of curvature. Principal focus (F) is the point on the principal axis, where a parallel beam of light, parallel to the principal axis after reflection converges in the case of a concave mirror and appears to diverge from in the case of a convex mirror. Focal length (f) is the distance of the principal focus from the pole of the mirror. Spherical mirrors can be further classified into the following two types as i. Concave mirrors ii . Convex mirrors. The images formed by the mirrors are of two types they are i. Real images ii. Virtual Images Real images are those that can be caught on a screen while virtual images are those that cannot be caught on a screen. Formation of Images by Spherical Mirrors The image formed by a convex mirror is always erect, virtual, and diminished in size. The location of the object does not affect the characteristics of the image. Thus, as the object approaches the mirror, the image approaches the mirror too but not proportionately. This is why, the rear view mirrors of the cars and bikes are made of convex mirrors. Hence, we have the caution “Objects seen in the mirror are closer than they appear” printed on the outside rear view mirrors of vehicles. Unlike in a convex mirror, the nature and size of the image in a concave mirror depends on the distance of the object from the mirror. Concave Mirror If a part of a hollow glass sphere is cut and the cut part of the sphere is coated outside with silver or similar material, then its inner surface reflects the entire light incident on it, and thus, forms a mirror. Since the inner surface is a concave surface, the mirror so formed is called a concave mirror. The geometric centre of a concave mirror is called its pole. The centre of the sphere from which concave mirror was cut is called the centre of curvature of the concave mirror. The distance from any point on the concave mirror to its centre of curvature is called the radius of curvature of the concave mirror. An imaginary line passing through the centre of curvature and the pole of the concave mirror is called principal axis of the concave mirror. The area of a concave mirror that is exposed to incident light is called the aperture of the concave mirror. The length along the principal axis from the pole to the principal focus is called the focal length of the concave mirror. If an object is placed close to a concave mirror such that the distance between the mirror and the object is less than its focal length, then a magnified and virtual image is formed. Due to this property, concave mirrors are used in many applications. A concave mirror can be used as a shaving mirror, and by dentists to view clearly the inner parts of the mouth. Concave mirrors converge the light incident on them and hence are called converging mirrors. We can observe ourselves magnified when the mirror is placed close to our face. This is due the position of the object between the focus and the pole. As the object moves away from the mirror, the size of its image reduces along with its distance from the mirror. If an object is placed close to a concave mirror such that the distance between the mirror and the object is less than its focal length, then a magnified and virtual image is formed. Due to this property, concave mirrors are used as shaving mirrors, and by dentists to view clearly the inner parts of the mouth. Reflection by Concave Mirrors Incident Ray Reflected Ray Parallel to principal axis Passes through focus Passes through C Retraces its path Passes through focus parallel to principal axis Strikes the pole at an angle eith principal axis Makes the same angle with principal axis Image Formation by Concave Mirror Depending on the position of the object in front of the concave mirror, the position, size and the nature of the image varies. Object at infinity A real, inverted, highly diminished image is formed at the focal point F, in front of the concave mirror. Object beyond C A real, inverted, diminished image is formed between C and F, in front of the concave mirror. Object at C A real, inverted, same sized image is formed at C, in front of the concave mirror. Object between C and F A real, inverted, enlarged image is formed beyond C, in front of the concave mirror. Object at F A real, inverted, highly enlarged image is formed at infinity, in front of the concave mirror. Object between F and P A virtual, erect and enlarged image is formed behind the concave mirror. Image Formation by a Concave Mirror Object Location Image Location Nature of Image Infinity At F • Real • Inverted • Highly Diminished Beyond C Beyond F and C • Real • Inverted • Diminished At C At C • Real • Inverted • Equal to size of object Between C and F Beyond C • Real • Inverted • Magnified At F Infinity • Real • Inverted • Highly Magnified Between F and P Behind the mirror • Virtual • Erect • Magnified Uses of Concave Mirrors Concave mirrors are used as shaving mirrors to see a larger image of the face. Dentists use concave mirrors to view a magnified view of the interior parts of the mouth are concave. ENT doctors use them for examining the internal parts of the ear, nose and throat. They are used as reflectors in the headlights of vehicles, search lights and in torch lights to produce a strong parallel beam of light. Huge concave mirrors are used to focus sunlight to produce heat in solar furnaces. Convex Mirror If the cut part of the glass sphere is coated from inside with silver or a similar material, then its outer surface reflects the entire light incident on it, and thus forms a mirror. Since the outer surface is a convex surface, the mirror so formed is called a convex mirror. The geometric centre of a convex mirror is called its pole. The centre of the sphere from which the mirror was cut is called the centre of curvature of the mirror. The distance from any point on the convex mirror to its centre of curvature is called the radius of curvature. An imaginary line passing through the centre of curvature and the pole of the mirror is called its principal axis. The reflected rays, when projected backwards, appear to meet at a point on the principal axis. This point is called the principal focus. The length along the principal axis from the pole to the principal focus is called the focal length. The area of a convex mirror that is exposed to incident light is called the aperture. If the aperture of a convex mirror is small, then its focal length is equal to half its radius of curvature. Convex mirrors diverge the light incident on them and hence they are called the diverging mirrors. Due to this they always form diminished, virtual and erect images irrespective of the position of the object in front of them. Thus, the magnification produced by these mirrors is always less than one. The field of view for a convex mirror is greater than that for a plane mirror, the aperture being the same. Hence, convex mirrors are used as rear-view mirrors in vehicles. It is also installed behind automated teller machines as a security measure. The field of view for a convex mirror is greater than that for a plane mirror, the aperture being the same. Hence, convex mirrors are used as rear-view mirrors in vehicles. It is also installed behind automated teller machines as a security measure. The images formed by convex mirrors are always diminished, virtual and erect, irrespective of the position of the object. Reflection by Convex Mirror Incident Ray Reflected Ray Parallel to principal axis Appears to pass through focus Directed towards the focus Appears to pass parallel to principal axis Strikes the pole at an angle eith principal axis Makes the same angle with principal axis Image Formation by Convex Mirror Irrespective of the position of the object, a virtual, erect and diminished image is formed between F and P, behind the convex mirror. Uses of Convex Mirrors Used as rear view mirrors in automobiles as it covers wide area behind the driver. Used as reflectors for street light bulbs as it diverges light rays over a wide area. Used as Rear view mirrors of vehicles and the ones used in ATM centres. Sign Convention for Spherical Mirrors Object is always considered at the left of mirror Distances measured along y-axis above the principal axis are taken as positive and that measured along y-axis below the principal axis are taken as negative. Distances measured in the direction of the incident ray are taken as positive and the distances measured in the direction opposite to that of the incident rays are taken as negative. All distances are measured from the pole of the mirror. Table Showing the Sign Convention Types of Mirror u v f R Height of the Object Height of the Image Real Virtual Real Virtual Concave mirror – – + – – + 123: nR3oTB2HywuKUQCXkJaiuA1PfjAFLEeFfThgg7o2gWz2eoIArTf9DjH8enJYtcAkeUDEv2CKQHEKJvz9u6g4R4idP1DTXs7uEyMD testt\ tests
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