Ray Diagram Ray Diagram • What is a ray diagram? • Important things to remember when making a Ray Diagram • Important Terms in the study or Ray Diagram • How to make a ray diagram: • Rules for drawing reference rays • Plane and Curved Mirrors (Concave and Convex Mirrors) • Lenses • Diverging Lenses • Converging Lenses Ray Diagram -a diagram that traces the path that light takes in order for a person to view a point on the image of an object. -a representation of the possible paths light can take to get from one place to another. This is often from a source or object to an observer or screen. Important things to remember when making a Ray Diagram • Light travels in straight lines within a uniform medium (this means that light can change direction upon entering a different medium) • Light has a direction of travel, it is often useful to indicate this with an arrow on your ray. • A sharp real image (an image that can be displayed on a screen) is formed when all rays from one point on an object all “appear”, to have come from one unique point on the image i.e. a straight line tracing back along their direction will always pass though this point. • For situations involving multiple lenses or mirrors, the image formed from one of these components can act as the object for another one. Important Terms to Remember Principal Axis – line that extends infinitely from the center of the mirrors surface through the center of curvature. Important Terms to Remember Center of Curvature- the center of the spherical shell of which the mirror is a small part. Important Terms to Remember Radius of Curvature – the same as the radius of the spherical shell in which the mirror is a small part. Important Terms to Remember Focal point (F)- a place between the center of curvature and the mirror Important Terms to Remember Real Image – can be displayed on a surface Important Terms to Remember Virtual image – appear behind a mirror Mirror Equation 1 1 1 = + 𝑓 𝑑𝑜 𝑑𝑖 Magnification ℎ𝑖 −𝑑𝑖 𝑚= = ℎ𝑜 𝑑𝑜 Ray diagram are useful for checking values calculated from the mirror and magnification equations Plane Mirror A mirror with a flat reflective surface. For light rays striking a mirror, the angle of reflection equal the angle of incidence. Plane Mirror Plane Mirror Spherical Mirrors When drawing ray diagrams for spherical mirrors, follow the basic procedure for a flat mirror, but also measure all distances along the principal axis and mark the center of curvature, C, and the focal point, F. Spherical Mirrors Three reference rays are used to find the image point. The intersection of any two rays locate the image. The third ray should intersect at the same point and can be used to check the diagram. Rules for drawing reference rays Ray Line drawn from the object to mirror Line drawn from mirror to image after reflection 1 parallel to principal through focal point, axis F 2 through focal point, parallel to principal F axis 3 through center of curvature, C back along itself through C Concave Spherical Mirror A spherical mirror with light reflecting from its silvered, concave surface. Concave spherical mirror are used whenever a magnified image of an object is needed. Concave Spherical Mirror C Concave Spherical Mirror When the object’s distance is greater than the focal length, p>f C F Characteristic of the Image 1. Real 2. Inverted 3. Reduced Concave Spherical Mirror When the object’s distance is equal to the focal length, p=f C F The image is infinitely far to the left and therefore is not seen Concave Spherical Mirror When the object lies between the focal point and the mirror surface C F Characteristic of the Image 1. Virtual 2. Upright 3. Enlarged Problem 1 A concave spherical mirror has a focal length of 10.0 cm. Locate the image of a pencil that is placed upright 30.0 cm from the mirror. Find the magnification of the image. Draw a ray diagram to confirm your answer. Solution: Given: f = +10.0 cm do = +30.0 cm Mirror Equation 1 1 1 = + 𝑓 𝑑𝑜 𝑑𝑖 1 1 1 = − 𝑑𝑖 𝑓 𝑑𝑜 1 1 1 = − 𝑑𝑖 10 30 1 1 = 𝑑𝑖 15 𝑑𝑖 = 15 𝑐𝑚 Magnification 𝑑𝑖 𝑀=− 𝑑𝑜 15 𝑀=− 30 𝑀 = −0.50 Sign Convention for Magnification Sign of M Orientation of image with respect to object Type of image this applies to + Upright Virtual - Inverted real Ray Diagram C F f = 10.0 cm do = 30.0 cm di = 15 cm Convex Spherical Mirror A convex spherical mirror is a segment of a sphere that is silvered so that light is reflected from the sphere’s outer convex surface. This type of mirror is also called a diverging mirror because the incoming rays diverge after reflections as though they were coming from some point behind the mirror. Convex Spherical Mirror C Convex Spherical Mirror Characteristic of the Image 1. Virtual 2. Upright 3. Reduced F C Convex Spherical Mirror The resulting image in a convex spherical mirror is always virtual and the image distance is always negative. Magnification is always less than 1. Problem 2 An upright pencil is placed in front of a convex spherical mirror with a focal length of 8.00 cm. An erect image 2.50 cm tall is formed 4.44 cm behind the mirror. Find the position of the object, the magnification of the image, and the height of the pencil. Solution Given: f = -8.00 cm q = -4.44 cm h’ = 2.50 cm 1 1 1 = − 𝑝 𝑓 𝑞 1 1 1 = − 𝑝 −8.00 −4.44 1 89 = 𝑝 888 𝑝 = 9.98 𝑐𝑚 Magnification 𝑞 𝑀=− 𝑝 −4.44 𝑀=− 10.0 𝑀 = 0.444 Height of the image: 𝑞 ℎ′ − = 𝑝 ℎ 𝑝ℎ′ ℎ=− 𝑞 9.98 2.5 ℎ=− = 5.62 𝑐𝑚 −4.44 Ray Diagram h = -5.62 cm h’ = 2.50 cm F f = -8.0 cm p = 9.98 cm q = -4.44 cm C Lenses When drawing ray diagrams for lenses, there are a few important things to note. Firstly, lenses can either be drawn as lens shapes or as lines with arrows on them. The convention is that a diverging lens has inwards pointing arrows and a converging lens has outwards pointing arrows, mimicking the shapes of the lenses. Diverging Conventional Lens Drawings Shorthand arrows Converging Converging Lenses F F Characteristic of the Image 1. Real 2. Inverted 3. Enlarged Diverging Lens F F Characteristic of the Image 1. Virtual 2. Upright 3. Reduced Rainbow formation Rainbow is an arc of colors appearing opposite the sun as a result of the refraction of sunlight in rain. How does a rainbow form? • Rainbows are created by sunlight and water droplets. • Rainbows are created by refraction and reflection of sun’s rays in falling rain or mist. • Sunlight strikes the front of raindrop and is refracted and separated into it’s colors. Then the light hit back the raindrop and is reflected, and is refracted again as it leaves the raindrop. What makes colors in the rainbow? • The sunlight consists of all wavelengths of visible light, which we simply see as white light because they are combined together. • When light is refracted, different wavelengths refract at different angles, therefore the various colors are separated. • Rainbows have 7 colors; however, they actually consist of every color. The color is constantly changing from red to violet.
