[Music] light reflection and refraction we all know that light is a form of energy it travels in a straight line in this chapter we are going to study the reflection and refraction of light what is reflection of light when a light Ray strikes a smooth polished surface like mirror it bounces back it is called as reflection of light we can study the reflection of light with the help of mirrors mirror is an OPAC object with shiny reflective surface it is because of the reflection of light we will be able to see our images in mirrors what is refraction of light when a light Ray passes from one medium to another medium its traveling speed changes and results in change of it its direction this phenomenon is called refraction of light a straw in a glass appears to be bent this is due to refraction of light we can study the refraction of light with the help of lens lens is a transparent object usually made of glass eyeglasses are the examples of lenses which use in our day-to-day life first let us study the reflection of light with the help of mirrors this is a plain mirror when a light Ray strikes a plain mirror it get reflected back according to the loss of reflection the angle of reflection is equal to the angle of incidence image formation plane mirrors create virtual images that appear to be located behind the mirror at the same distance as the object in front of the mirror these virtual images are not real that means they cannot be projected onto a screen they are formed by the apparent intersection of reflected light rays when extended backward size and magnification the size of the image in a plain mirror is the same as the size of the object there is no magnification means that objects in a plain mirror appears to be the same size as they are in reality laterally reversed the images formed by plain mirrors are laterally reversed also known as Left Right reversed this means that if you raise your right hand in front of a plain mirror your image will appear to raise its left hand now let us understand the reflection of light by spherical mirrors a spherical mirror is a curved mirror and it forms the part of a sphere spherical mirrors are of two types one convex mirrors and two concave mirrors a convex mirror is a type of a spherical mirror that has an outward curved reflective surface a concave mirror is a is a type of a spherical mirror that has an inward curved reflective surface to understand Reflection by sperical mirror we need to know certain terms pole the center point of the reflecting surface of a spherical mirror is called pole it lies on the surface of the mirror pole is denoted by letter P Center of curvature the center of curvature is the center of the imaginary sphere from which the spherical mirror is derived it lies behind the mirror in case of a convex mirror and lies in front of the reflecting surface of a concave mirror it is represented by the letter c radius of curvature the radius of curvature R of a spherical mirror is the radius of imaginary sphere of which mirror is a part principal axis the line joining pole and center of curvature is called principal axis we should remember that the principal is normal to the mirror at at its pole that means at the point of pole the angle between the plane of the mirror and the principal axis is 90° principal Focus if a number of light rays parallel to the principal axis are falling on a concave mirror they all meet or intersect at a point on the principal axis of the mirror this point is called the principal focus of the concave mirror in case of a convex mirror the reflected Rays appear to come from a point on the pr principal axis this point is called the principal focus of the convex mirror the principal focus is represented by the letter F focal length the distance between the pole and the principal focus of a spherical mirror is called the focal length and it is represented by the letter small F aperture the diameter of the reflecting surfaces of the spherical mirror is called its aperture in this chapter we are discussing about the spherical mirrors whose aperture is smaller than their radius of curvature let us see the relation between the radius of curvature and the focal length the relationship between the radius of curvature R and the focal length F of a spherical mirror is as follows for spherical mirrors with small apertures the radius of curvature is found to be equal to twice the focal length we write it as R = to 2f or FAL to RX 2 this means that the principal focus of a spherical mirror lies midway between the pole and the center of curvature representation of images formed by spherical mirrors using Ray diagrams rules for making Ray diagrams parallel Ray rule for a concave mirror if a light Ray passes parallel to the principal axis after reflecting it passes through the focal point f for a convex mirror if a light Ray passes parallel to the principal axis after reflecting it appears to come from the focal point F behind the mirror focal Ray rule for a concave mirror if a light Ray passes through principal Focus after reflection it emerges parallel to the principal axis for a convex mirror if a light Ray is directed towards the principal Focus after reflection it emerges parallel to the principal Axis Center of curvature Ray rule for a concave mirror if a light ray goes from the object to the center of curvature after reflection it retraces its path back to the center of curvature for a convex mirror if a light Ray is directed in the direction of center of curvature after reflection it retraces its path back four array incident oblique to the principal axis towards pole of the mirror is reflected obliquely on the concave mirror or a convex mirror the incident and reflected Rays making equal angles with the principal axis first let us draw some R diagrams image formation by a concave mirror for different positions of the object case one if the position of the object is at the Infinity the position of the image will be at the focus F the size of the image is highly diminished and point sized the nature of the image is real and inverted case two if the position of the object is beyond C the position of the image will be between F and C the size of the image is is diminished the nature of the image is real and inverted case three if the position of the object at C the position of the image will be at C the size of the image will be same as object the nature of the image is real and inverted case four if the position of the object is between C and F the position of the image will be at Beyond C the size of the image will be nlog the nature of the image is real and inverted case five if the position of the object is at F the position of the image will be at Infinity the size of the image will be highly enlarged and the nature of image is real and inverted case six if the position of the object is between P and F the position of the image will be behind the mirror the size of the image will be enlarged and the nature of image is virtual and direct uses of concave mirrors concave mirrors are used as shaving mirrors dentist mirrors they're also used in the reflectors of torch lights and vehicle lights now we will see the image formation by concave mirror here we consider only two positions of the object for studying the image formed by concave mirror case one if the position of the object is at Infinity the position of the image will be at the focus behind the mirror the size of the image is highly diminished and point sized the nature of the image is virtual and direct case two if the position of the object is between infinity and the pole of the mirror the position of the image will be between P and F behind the mirror the size of the image is diminished the nature of the image is virtual and erect uses of convex mirrors they are used as rear view mirrors in vehicles because they always forms an erect image and have wider field of view as they are curved outwards sign convention for Reflection by spherical mirror the sign convention for spherical mirrors is a set of rules used to determine the sign either positive or negative of various distances and quantities involved this convention is important for calculating the image distances object distances and to find magnification object placement the object is always placed to the left of the mirror indicating that the light from the object approaches the mirror from the left side measurement from the pole distances parallel to the principal axis are measured from The Mirror's pole the pole is the point where the mirror surface intersects the principal axis direction of measurement all distances measured to the right of the orig along the positive x-axis are considered positive while those measured to the left of the origon along the negative xaxis are considered negative this helps in determining the position of the object and image relative to the mirror height above the principal axis distances measured perpendicular to and above the principal axis along the positive y- AIS are considered positive this is used to determine the heights of the objects and images above or below the principal axis height below the principal axis distances measured perpendicular to and below the principal axis along the negative y-axis are considered negative this convention ensures that Heights below the principal axis are assigned negative values these sign conventions are fundamental for analyzing and solving problems related to spherical mirrors mirror formula and magnification the mirror formula is particularly useful for determining the position and characteristics of an image formed by a mirror the mirror formula is a fundamental equation used to relate the object distance U and the image distance V and the focal length F of a spherical mirror it is expressed as 1X V + 1 by U is equal to 1x F where f is the focal length of the mirror V is the image distance means the distance from the mirror to the image and U is the object distance that is the distance from the mirror to the object magnification magnification refers to the ratio of an image to the height of an object it is denoted by letter M that means it is the comparision of the size of the image with respect to the size of the object that is height of the image h-h by height of the object h means m is equal to h- by h the height of the object should be taken as positive since it is usually placed above the principal axis the height of the image should be taken as positive if the image is virtual and should be taken negative if the image is real that means if the image is on the side of the object we can also find magnification by comparing the image distance and object distance we know that image distance means the distance between the mirror and the image and object distance means the distance between the mirror and the object so magnification is equal to image Distance by object distance that means m is equal to- V by U refraction of light refraction is the change in the direction of light passing obliquely from one medium to another medium refraction occurs due to change in the speed of light as it enters from one transparent medium to another the speed of light is more in air whereas the speed of light in water is less compared to air so the light Ray when it enters from air to water it bends towards the normal the refracted Ray is closer to the normal when compared to the incident Ray in our day-to-day life we see different phenomenon like pencil appears displaced when it partly immersed in glass of water in the same way a lemon kept in water in a glass tumbler appears to be bigger than its actual size the letters appears to be rised when seen through a glass laab placed over it these are all because of refraction of light these observations tell us that light does not travel in the same direction in all media refraction through a rectangular glass lab let us take a glass lab and pass a light Ray obliquely from one of its side the light Ray bends towards the normal and when it emerges out from the glass lab it bends again and moves away from the normal here we can observe that the angle of incidence at the air glass interface is equal and opposite to the angle of emergence at the glass air interface this is why the emergent Ray is parallel to the incident Ray loss of refraction of light one the incident Ray the refracted Ray and the normal to the interface of two transparent media at the the point of incidence all lie in the same plane two the ratio of s of angle of incidence to the sign of angle of refraction is a constant for the given pair of media this law is also known as Snell's law of refraction if I is the angle of incidence and R is the angle of refraction then sin I by sin r equal to constant refractive index the refractive index of a medium is a measure of how much the speed of light is reduced when it passes through that Medium compared to its speed in vacuum it is a dimensionless quantity and a higher refractive index indicates a slower speed of light in that medium light travels faster in vacuum with a speed of 3 into 10 ^ of 8 Ms to the^ minus1 in air the speed of light is only marginally less compared to that in vacuum it reduces considerably in glass or in water the value of of refractive index for a given pair of media depends upon the speed of light in the two media a ray of light traveling from medium 1 into medium 2 let V1 be the speed of the light in medium 1 and vs2 be the speed of the light in medium 2 the refractive index of medium 2 with respect to medium 1 is given by the ratio of the speed of light in medium 1 and the speed of light in medium 2 this is usually represented by the symbol n21 the this can be expressed as n21 equal to speed of light in medium 1 by speed of light in medium 2 that means V1 by vs2 the refractive index of medium 1 with respect to medium 2 is represented as n12 it is given as n12 equal to speed of light in medium 2 by speed of light in medium 1 that means vs2 by V1 if medium 1 is vacuum or air then the refractive index of medium 2 is considered with respect to vacuum this is called the absolute refractive index of the medium it is simply represented as N2 if C is the speed of light in air and V is the speed of light in the medium then the refractive index of the medium NM is given by NM equal to speed of light in air by speed of light in medium that is C by V different materials have different refractive indexes for example the refractive index of water is approximately 1.33 while the refractive index of diamond is approximately 2.42 now let us see the refraction by spherical lenses a transparent material Bound by two surfaces of which one or both surfaces are spherical forms spherical lens they can be either convex lens or concave lens based on their shape and refractive properties a convex lens also known as converging lens it is a transparent material with curved surfaces it is thicker at the center and thinner at the edges convex lens are designed to converge or Focus parallel incident light rays to a single point called the focal point a concave lens also known as diverging lens is a transparent Optical device with curved surfaces that curve inward like a cave concave lenses are thinner at the center and thicker at the edges these lenses are designed to cause parallel incident light rays to diverge away from the virtual focal point a lens has two spherical surfaces each surface forms a part of a sphere the center of these spheres is called Center of curvature principal axis an imaginary straight line passing through the two centers of curvatures of a lens is called its principal axis optical center o the central point of a lens is called optical center aperture effective diameter of the circular outline of a spherical lens is called its aperture principal Focus F the point where the Rays parallel to the principal axis meet after refraction is called principal focus a lens has two spherical folai focal length F the distance of principal Focus from Optical Center rules for the ray diagram of spherical lens a light Ray which is parallel to the principal axis after refraction will pass through the principal axis in case of convex lens and will appear to be coming from Principal Focus in case of concave lens light rays passing through the convex lens are directed towards the focus in concave lens will emerge parallel to principal axis a ray directed to the optical center will emerge out undeviated in case of both convex and concave lens image formation by convex lens case one if the position of the object is at Infinity the position of the image will be at the focus FS2 and the relative size of the image is highly diminished and point sized the nature of the image is real and inverted case two if the position of the object is at Beyond 2 F1 the position of the image will be between F2 and 2 F2 the relative size of the image is diminished the nature of the image is real and inverted case three if position of the object is at 2f1 the position of the image will be at 2f2 the relative size of the image is same the nature of the image is real and inverted case 4 if position of the object is at F1 and 2f1 the position of the image will be at beyond 2f2 the relative size of the image is enlarged the nature of the image is real and inverted case five if position of the object is at Focus F1 the position of the image will be at Infinity the relative size of the image is infinitely large and highly enlarged the nature of the image is real and inverted case six if position of the object is between Focus F1 and optical center o the position of the image will be on the same side of the lens as the object the relative size of the image is enlarged the nature of the image is virtual and erect let us now study the nature position and relative size of the image formed by a concave lens case one if position of the object is at Infinity the position of the image will be at the focus F1 the relative size of the image is highly diminished and point sized the nature of the image is virtual and erect case two if the position of the object is between infinity and optical center o of the lens the position of the image will be between focus and optical center o the relative size of the image is diminished the nature of the image is virtual and direct s Convention of spherical lens the sign Convention of the spherical lens is same as the one used for spherical mirrors we apply the same rules for signs of distances except that all measurements are taken from the optical center of the lens in the S Convention of spherical lens the focal length of a convex lens is positive and that of a concave lens is negative lens formula this formula gives the relationship between object distance U and image distance V and the focal length F the lens formula is expressed as 1X V - 1 by U = to 1x F the magnification M of a spherical lens is a measure of how much the lens magnifies or reduces the size of an object as it forms an image magnification is calculated using the following formula M = h- by H magnification is represented by the the letter M if H is the height of the object and h- is the height of the image given by a lens magnification produced by a lens is also related to the object distance U and the image distance V this relationship is given by m is equal to h- by H = to V by U where m is the magnification of the lens V is the image distance means the distance from the lens to the image and U is the object distance means the distance from the lens to the object power of lens the power of a lens is a measure of its ability to bend light it is represented by the letter P the power P of a lens of focal length f is given by P = 1X F the power of a lens is measured in units called diopters d p is the power of the lens in diopters d f is the focal length of lens in meters y positive and negative Powers a lens with a positive power is called a converging lens which focuses light rays to a point convex lenses have positive Powers a lens with a negative power is called diverging lens which causes light rays to spread out concave lenses have negative Powers this is all about the reflection and refraction of [Music] light [Applause] [Music]