Module 1 Reflection and Refraction PDF

Module 1 Reflection and Refraction Mirrors: Mirrors are made into different shapes for different purposes. The two of the most prominent types of mirrors are Plane Mirrors and Spherical Mirrors. A plane mirror is a flat, smooth reflective surface....

Module 1 Reflection and Refraction Mirrors: Mirrors are made into different shapes for different purposes. The two of the most prominent types of mirrors are Plane Mirrors and Spherical Mirrors. A plane mirror is a flat, smooth reflective surface. A plane mirror always forms a virtual image that is upright and of the same shape and size as the object, it is reflecting. A spherical mirror is a mirror that has a consistent curve and a constant radius of curvature. The images formed by a spherical mirror can either be real or virtual. Spherical mirrors are of two types Concave Mirror and Convex Mirror Spherical mirrors are the mirrors having curved surfaces that are painted on one of the sides. Spherical mirrors in which inward surfaces are painted are known as convex mirrors. Spherical mirrors in which outward surfaces are painted are known as concave mirrors. Reflection at plane surfaces (mirrors): Any smooth surface acts as a mirror. A mirror may be plane or curved. Mirrors were usually made in the past, by coating glass with silver. Nowadays, they are made by depositing in vacuum a thin film of aluminum on a polished surface. The reflecting film is protected by deposition of a thin layer of silicon monoxide or magnesium fluoride over it. The plane mirrors used as looking glass are coated at the back so that the reflecting layer is completely protected. The mirrors used for technological purposes are coated on the front surface so that losses in energy due to transmission through the substrate material are reduced. 1 Object and Image: An object is anything from which light rays radiate. This light could be emitted by the object itself or reflected from it. There are two kinds of objects, a point object, which has no physics extent and an extended or distributed object, which has a length, width and height. When light rays proceeding from an object are reflected at a mirror, they converge to or appear to diverge from a position different from that of the original object and give the impression of object being there. The apparent object as seen by the observer is called the image of the object. The image formed by an optical component may be real or virtual. The eye sees a virtual image as well as it sees a real image. A real image contains light energy; the image can be received and seen on a screen. And also, the image can be photographed by simply placing a photographic film (or plate) at the position of the image. Real images are essential for photography. A virtual image cannot be received on a screen. The light rays never actually pass through the virtual image; hence, the image cannot be received on a screen. For the same reason, it cannot be recorded on a photographic plate placed at its position. Virtual image can be photographed only with the help of a converging optical system, which uses the virtual image as a virtual object and forms its real image. Image of a point object: Image formation by mirrors involves only the law of reflection. A point object O located at a distance u in front of a plane mirror. u is called the object distance. The ray OA is incident normally on the mirror and is reflected along its original path. The ray OB makes an angle i and is reflected at an equal angle with the normal. Extend the two reflected rays backward, they intersect at point I, at a distance v behind the mirror. v is the image distance. Point I is the image of the object point O. The image is virtual because no rays actually come from it. The two triangles OAB and IAB are congruent, so O and I are at equal distances from the mirror, u and v have equal magnitudes. It means that the image point I is located exactly opposite the object point O and is far behind the mirror as the object point is from the front of the mirror. The object distance u is positive because the object point is on the incoming side of the reflecting surface. The image distance v is negative because the image point I is the right side of the mirror. 2  The object and image distances are related as u=-v Image of an extended object: An arrow AB of height h. the image formed by such an extended object is an extended image, to each point of on the object, there corresponds to a point on the image. The ray BD is incident normally on the mirror and is reflected along the path DB. The ray BC, incident on the mirror at an angle i, is reflected at an equal angle along CQ. These two rays from B appear to diverge from the image point after B' after reflection. The image of the arrow is the line A'B', with height h'. Other points of the object AB have image points between A' and B'. The triangles ABC and A'B'C' are congruent, so the object AB and image A'B' have the same size and orientation and h=h'. So the image is erect. The ratio of image height to the object height is called lateral magnification h m= h The lateral magnification for a plane mirror is always +1. 3 Properties of image in plane mirrors: 1. Image formed by a plane mirror is virtual and erect. 2. The image is as far behind as the object is in front of it. 3. The right side of the object is transformed into left side of the image. 4. Magnification produced by a plane mirror is unity. Hence, the image is as large as the object. 5. When a plane mirror is rotated through a certain angle, the reflected ray turns through twice the angle. 6. If an object is held between two or more plane mirrors, multiple virtual images are 360 formed. The number of image is given by N = − 1 , where α is the angle between  the mirrors. Reflection at spherical mirrors: Mirrors need not have to be always flat, they may be curved. Spherical mirrors are of the simple type among the curved mirrors. A spherical mirror is a segment of a spherical surface and usually has circular edges. There are two types of spherical mirrors, concave and convex mirrors. When the reflection takes place from the inner surface of the spherical segment, then the mirror is called concave mirror. If light is reflected from the outer bulging surface of the spherical segment, then the mirror is called a convex mirror. The laws of reflection are equally applicable to the curved mirrors. Using these laws, we can find out the nature and position of the image when the object is situated at different distances from the mirror, we can also determine the relation between the distance of the object and image and the focal length of the mirror. Basic terms: 1. Centre of curvature: The centre of curvature (C) is the centre of the sphere of which the mirror is a small segment. 2. Vertex: The vertex (pole) is the midpoint of the mirror. 3. Radius of curvature: The radius of curvature (R) is the radius of the sphere of which the mirror is a small section. 4. Principal axis: The principal axis is the line passing though the centre of curvature (C) and the vertex. It extends indefinitely in both directions. 5. Principal focus: With a concave mirror, all rays parallel to the principal axis pass through a single point after reflection. F is called the principal focus. The parallel rays 4  converge to F after reflection. However, in case of a convex mirror, the reflected rays appear to emerge from behind the mirror. Thus, the reflected rays appear to diverge from the principal focus. 6. Focal plane: The focal plane is a plane passing through the point and perpendicular to the principal axis. 7. Focal length: The focal length of the mirror is the distance, between the vertex P and the principal focus. It will be shown later that f=R/2. 8. Power: the reciprocal of the focal length is called the power of the mirror. Thus P=1/f. 9. Aperture: The diameter of the circular outline of the mirror is called aperture of the mirror. The unobstructed surface area of the mirror, having circular rim and available for reflection, represents the aperture. It is measured in terms of the angle θ, subtended by the extremities of the mirror at the centre of curvature. The aperture determines the amount of light energy that received by mirror. In other words, it determines the light gathering capability of the mirror. Paraxial rays and paraxial approximation: A ray is said to be paraxial if the angle θ between the ray and the principal axis (or symmetry axis) is small. Only rays inclined at less than about 10° to the principal axis are considered as paraxial rays and they lie close to the axis thought out the distance from object to image. As the angles are small and when expressed in radians, we can set the cosines equal to unity and the sines and tangents equal to the angles. This is known as the small angle approximation. Accordingly we can set cos   1 for cosθ sin    for sinθ tan    for tanθ This is also known as paraxial approximation. As we are approximating sin θ to θ, paraxial approximation is also celled as the first order theory. A small area in the immediate surroundings of the optical axis is known as the paraxial region. Gauss, in 1841, was the first to give a systematic analysis of the formation of images under paraxial approximation. The results are known as first order paraxial or Gaussian optics. Sign Convention: To specify the position of the object and the image, we used a reference point and sign convention. The widely used, easy remember and simplest convention is Cartesian sign convention. 5  1. The diagrams are drawn with the incident light travelling from left to right. 2. The distances are measured by taking the vertex as the origin. 3. The distances measured in the direction of the incident light are considered positive while those measured in the direction opposite to the incident light are taken as negative. 4. Heights measured upward and perpendicular to the principal axis are taken as positive while those measured down ward are considered negative. 5. Angles measured clockwise, beginnings at the optic axis, are negative. Angles measured counterclockwise are positive. Refraction of light: A light ray that travels through a parallel sided transparent slab is refracted at both faces. The two refractions at the parallel surfaces result in a sideways displacement but do not change the direction of the ray. At the first face, the Snell’s law takes the form 1 sin 1 = 2 sin 2 Because the faces are parallel, the angle of incidence for the second face is equals to θ2 and according to Snell’s law 2 sin 2 = 1 sin 3 By comparing both the equations 1 = 3 6  When the light ray passes through a parallel sided slab, the emergent ray is parallel to the incident ray. The net effect of the two refractions is a parallel displacement of the ray. The distance x between the incident and emergent ray is given by t.sin( 1 −  2 ) x= cos 2 Where t is the thickness of the glass slab, for small angles θ1 and θ2 measured in radians   −1 It can also be shown that x = t      Apparent depth: Let an object lie in below a refractive medium of refractive index µ2 and is seen almost normally in a medium of refractive index µ1. According to Snell’s law, 2 sin i = 1 sin r AB AB 2 = 1 OB IB Let OB=u and IB=v. Then  2 v = 1u 1 v= u 2 If µ2 > µ1, v n2 3. The angle of incidence (i) must be greater than the critical angle (θc) i.e. i > θc. n  4. The critical angle c = sin −1  2   n1  Let n1 and n2 be the refractive indices of two media such that n1>n2. When a ray of light travelling in a medium of higher refractive index n1 strikes a second medium of lower refractive index n2 making an angle of incidence i with the normal, this ray is refracted into the second medium with angle of refraction r and moves away from the normal. The refracted ray bends away from the normal as it travels from denser to rarer medium with increase of angle of incidence ‘i’. In this we get three cases Case 1: When i