Mirrors PDF

Reflection of Light and Mirrors What is reflection? Reflection is the bouncing back of light into the same medium it has been traveling before striking a surface. THE LAWS OF REFLECTION There are 2 types of reflection. Reflection from smooth surfaces is called regular or specular refle...

Reflection of Light and Mirrors What is reflection? Reflection is the bouncing back of light into the same medium it has been traveling before striking a surface. THE LAWS OF REFLECTION There are 2 types of reflection. Reflection from smooth surfaces is called regular or specular reflection. Reflection from rough surfaces is called diffuse reflection. Each individual ray for each type of reflection obeys the following laws of reflection. 1. The angle of incidence is equal to the angle of reflection. (θi = θr ) 2. The incident ray, normal and the reflected ray lie on one plane. - When a group of parallel rays strikes a smooth flat surface, the reflected rays are parallel to one another. - When a group of parallel rays strikes a rough surface, normal at the point of incidence is different at each ray. - Consequently, , when the individual rays are reflected from the surface, they will be scattered in different directions. - The rays cannot be parallel to each other. What is a mirror? -A mirror is a reflective surface that light does not pass through, but bounces off and this produces an image. TYPES OF MIRRORS Plane Mirrors - A mirror with a flat surface. - The ordinary mirror you use at home is a plane mirror Spherical Mirrors - A spherical mirror has a reflecting surface taken from the surface of a sphere. - It may be concave or convex. Concave Mirror - A concave mirror curves inward in the direction of incident rays. Concave Mirror Convex Mirror - A convex mirror bulges outward to the incident rays. Convex Mirror Images produced by Mirrors images produced by a mirror may be real or virtual. Real Image - A real image is formed by actual intersection of reflected rays. - It forms in front of the mirror and is always upside down relative to the object. - It can projected on a screen placed in front of the mirror. Virtual Image - A virtual image is formed behind the mirror and is upright relative to the object. - There is no actual intersection of the reflected rays, but if you extend the rays as if they came come behind the mirror, there is an intersection. Virtual Image - Since they are not formed by actual rays, they cannot be projected on a screen. Image formed by a Plane Mirror - The image formed by a plane mirror is always virtual, upright, and the same size as the object, located in the same distance behind the mirror, and laterally reversed. Suppose that you are standing in front of the plane mirror in your house. You are 1.5 m away from the mirror. How far will your image be away from you? Plane mirrors in a beauty salon are arranged in such a way that they face each other. Suppose that the two mirrors are 2.0 m apart and an object is placed 0.5 m from one of the mirrors. Find the distance of the first image formed by each mirrors. Spherical Mirrors - Spherical Mirrors are mirrors cut out from a spherical reflecting surface. - There are 2 types of spherical mirrors: Concave and convex. Terms we may encounter in spherical mirrors -The center of curvature (C) is the center of the sphere from where the mirror was taken. Terms we may encounter in spherical mirrors - The vertex (V) is the center of the mirror. Sometimes called the pole of the mirror. - The radius of curvature ( R ) is the radius of the sphere. The distance between C and V. - The principal axis or optic axis is a straight line Terms we may encounter in spherical mirrors - The aperture is the width of the mirror. - The principal focus or focal point is the point between C and V. - The focal length is the distance between the vertex and focal point. Spherical Mirrors Image formed by a Convex Mirror - Virtual, upright and smaller than the object. Type Of Image Formed By Concave Mirrors At Different Object Positions. Image is located at F, the image is real, inverted, very small. Ray Diagram (Object beyond C, at C and between C and F. ) 1. Draw a line from the top of the object parallel to the principal axis towards the mirror. The ray will reflect through the focal point. 2’. Draw another line from the object through the focus, when it hit the mirror the ray will reflect parallel to the principal axis. Type Of Image Formed By Concave Mirrors At Different Object Positions. Image is located between C and F. Image is real, inverted and smaller than the object. Type Of Image Formed By Concave Mirrors At Different Object Positions. Image is located at C. The image is real, inverted and same size as the object. Type Of Image Formed By Concave Mirrors At Different Object Positions. Image is located beyond C. The image is real, inverted and bigger than the object. Ray Diagram (Object at F) 1. Draw a line from the top of the object parallel to the principal axis towards the mirror. The ray will reflect through the focal point. 2. A line drawn from C will be reflected on itself. Type Of Image Formed By Concave Mirrors At Different Object Positions. Image at infinity. No image formed because all reflected rays are parallel. Ray Diagram (Object between F and V) 1. Draw a line from the top of the object parallel to the principal axis towards the mirror. The ray will reflect through the focal point. 2. A line drawn from C will be reflected on itself. Type Of Image Formed By Concave Mirrors At Different Object Positions. Image located at the back of the mirror. Image is virtual, upright, and bigger than the object. Mirror Equation Ray diagrams are useful for determining the general location and size of the image formed by a mirror. However, the mirror equation and magnification equation give a more accurate mathematical description of the image Mirror Equation f- focal length of the mirror do – object distance di – image distance Mirror Equation Sign Convention for spherical mirrors Focal length f is + for a concave mirror f is – for a convex mirror Object distance do is + if object is in front of mirror do is – if object is behind the mirror Sign Convention for spherical mirrors Image distance di is + if image is real (in front of mirror) di is – if image is virtual (behind the mirror) Magnification m is + if the image is upright (w/r/t object) m is – if the image is inverted (w/r/t obj) Example: An object is placed 20.0 cm in front of a concave mirror of radius 50.0 cm. (a) What is the focal length of the mirror? (b) Where is the image located? (c) Characterize this image. Given: R= 50.0 cm do = 20.0 cm Solution: a. f= R/2 Example: b. Use the mirror equation and substitute the values. 1/25.0= 1/20.0 + 1/ di di = -100.0 cm The negative sign of di indicates the image is virtual. Example: Solve for magnification to know the relative size of the object. M= - di /do M= -(-100.0 cm/ 20.0 cm) M= 5.0 Image is upright and 5 times larger than the object. Example: An object is placed 10 cm from a concave mirror. The focal length is 5 cm. Determine (a) The image distance (b) the magnification of image Given: f = 5 cm do =10 cm Solution: a. 1/f = 1/ di + 1/ do 1/ di = 1/f - 1/ do Example: An object is placed 10 cm from a concave mirror. The focal length is 5 cm. Determine (a) The image distance (b) the magnification of image Given: f = 5 cm do =10 cm Solution: a. 1/f = 1/ di + 1/ do 1/ di = 1/5 - 1/10 = 1/10 1/ di = 1/f - 1/ do di = 10 cm Example: Solve for magnification to know the relative size of the object. M= - di /do M= -10 / 10 M= -1 cm Notes:  Ray diagrams visually shows the location, size and orientation of the image.  The use of mirror equation and magnification mathematically describe the location, size and orientation of the image.  Magnification is equal to 1 which means that the image is the same size as the object.  Focal length is half of radius.