THEORIES OF LIGHT Is light a wave or a stream of particles? Lets first analyze characteristics behaviors of light as a wave: All waves are known to undergo reflection or the bouncing off of an obstacle. All waves are known to undergo refraction when they pass from one medium to another medium. Diffraction involves a change in direction of waves as they pass through an opening or around an obstacle in their path. Wave interference is a phenomenon that occurs when two waves meet while traveling along the same medium. Polarized light waves are light waves in which the vibrations occur in a single plane. The process of transforming un-polarized light into polarized light is known as polarization. Now what about the particle-like behavior? The photoelectric effect is observed when light of a certain frequency strikes a metal and ejects electrons. Phenomenon Can be explained in terms of waves. Can be explained in terms of particles. Reflection Refraction Interference Diffraction Polarization Photoelectric effect THEORIES OF LIGHT Newton's theory - light consists of particles called corpuscles; this theory only explained reflection and refraction. Wave theory of light (Maxwell's theory) - light behaves like a wave; this explained all the properties of light such as reflection, refraction, diffraction, interference and polarization; it did not explain the photoelectric effect or radiation produced by an incandescent light. Quantum theory - light has a dual nature: when light is transmitted through space or matter, it behaves like a wave; when light is emitted or absorbed, it behaves like a particle called a photon. ELECTROMAGNETIC WAVES Electromagnetic waves are waves that are capable of traveling through a vacuum. They consist of oscillating electric and magnetic fields with different wavelengths. The wave speed equation is: c = f where c is the speed of light. The Electromagnetic Spectrum Wavelengths REFLECTION OF LIGHT Light obeys the law of refection that states that: "The angle of incidence is equal to the angle of reflection." Angle of Reflection = Angle of Incidence Angles are measured with respect to the normal line Light reflection from a smooth surface is called regular or specular reflection. Light reflection from a rough or irregular surface is called diffuse reflection. FLAT MIRRORS A flat mirror reflects light rays in the same order as they approach it. Flat mirrors are made from pieces of plate glass that have been coated on the back with a reflecting material like silver or aluminum. The image is the same size as the object and the same distance behind the mirror as the object is in front of the mirror. These images which appear to the eye to be formed by rays of light but which in truth do not exist are called virtual images. On the other hand real images are formed when rays of light actually intersect at a single point. Notice that the images formed by a flat mirror are, in truth, reflections of real objects. The images themselves are not real because no light passes through them. Left-Right Reversal CURVED MIRRORS A curved mirror is a mirror that may be thought of as a portion of a reflecting sphere. If the inside of the spherical surface is the reflecting surface, the mirror is said to be concave or converging. If the outside portion is the reflecting surface, the mirror is convex or diverging. A curved mirror has a geometric center or vertex A. The center of curvature or radius C. The focal length f of the mirror is half the radius: IMAGES FORMED BY CURVED SPHERICAL MIRRORS The best method of understanding the formation of images by mirrors is through geometrical optics or ray tracing. Ray 1. A ray parallel to the mirror axis passes through the focal point of a concave mirror or seems to come from the focal point of a convex mirror. Ray 2. A ray that passes through the focal point of a concave mirror or proceeds toward the focal point of a convex mirror is reflected parallel to the mirror axis. Ray 3. A ray that proceeds along a radius of the mirror is reflected back along its original path. 23.1 a. Find the images formed by the following mirrors using the Ray Tracing method. b. Write the characteristics of each image: real or virtual, larger, smaller or same size as object and inverted or upright. Convex Mirrors No image is formed. CONCAVE MIRROR IMAGES CONCAVE MIRROR IMAGES 3-D CONCAVE MIRRORS ARE CONVERGING CONVEX MIRRORS ARE DIVERGING THE MIRROR EQUATION The mirror equation can be used to locate the image: The ratio M is called the magnification, h o is the objects size and h i is the image size. Where d o is the objects distance, d i is the image distance and f is the focal length. R radius of curvature + converging- diverging f focal length + converging- diverging dodo object distance + real object didi image distance + real images - virtual images hoho object size+ if upright- if inverted hihi image size+ if upright- if inverted The Mirror Equation: Similar triangles: h o /(- h i ) = (d o - f) / f (1) Recall: h o / h i = -d o / d i (2) Combine (1) and (2): 1/d o + 1/d i = 1/f Mirror Magnification Equation: Triangles are similar: h o / (-h i ) = d o / d i Magnification m = h i / h o M = -d i /d o 23.2 Suppose you place a 5.0 cm tall spring in front of a concave mirror. The mirror has a focal length of 24 cm. The spring forms an image that appears to be at the same position as the spring, but the image is inverted. a. Where did you place the spring? h o = 5 cm f = 24 cm d o = d i d o = 2f = 2(24) = 48 cm b. How tall is the springs image? h o = 5 cm h i = -h o = - 5 cm 23.3 Suppose you are 19 cm in front of the bell of your friends trumpet and you see your image at 14 cm. Treating the trumpets bell as a concave mirror, what would be its focal length and radius of curvature? d o = 19 cm d i = 14 cm = 8.06 cm R = 2f = 2(8.06) = 16.1 cm 23.4 When you hold a convex mirror 21 cm from your eye, your image forms 7.0 cm behind the mirror. a. What is the magnification of the image? d o = 21 cm d i = - 7 cm = +0.33 b. What is the mirrors focal length and radius of curvature? d o = 21 cm d i = - 7 cm = cm R = 2f = 2(-10.5) = -21 cm REFRACTION The bending of a ray of light as it passes from one medium to another is called refraction.refraction. Reflection and Refraction at an Interface The speed of light c in a material is generally less than the free-space velocity c of 3 x10 8 m/s. In water light travels about three-fourths of its velocity in air. Light travels about two-thirds as fast in glass. The ratio of the velocity c of light in a vacuum to the velocity v of light in a particular medium is called the index of refraction n for that material. Light bends toward the normal when entering medium of higher index of refraction Light bends away from the normal when entering medium of lower index of refraction SNELLS LAW The ratio of the sine of the incident angle to the sine of the refracted angle is constant. n 1 sin 1 = n 2 sin 2 n 1 = index of refraction of the incident medium n 2 = index of refraction of the second medium 23.5 The speed of light in a plastic is 2 x10 8 m/s. What is the index of refraction of the plastic. v = 2 x10 8 m/s c = 3x10 8 m/s = 1.5 23.6 A ray of light travels from air into liquid. The ray is incident upon the liquid at an angle of 30. The angle of refraction is 22. a. What is the index of refraction of the liquid? n 1 = 1 1 = 30 2 = 22 n 1 sin 1 = n 2 sin 2 = 1.33 b. What might the liquid be? water THIN LENSES Lenses are an essential part of telescopes, eyeglasses, cameras, microscopes and other optical instruments. A lens is usually made of glass, or transparent plastic. A converging (convex) lens is thick in the center and thin at the edges. A diverging (concave) lens is thin in the center and thick at the edges. The two main types of lenses are convex and concave lenses. The focal length (f) of a lens depends on its shape and its index of refraction. Ray 1. A ray parallel to the axis passes through the second focal point F 2 of a converging lens or appears to come from the first focal point F 1 of a diverging lens. Ray 2. A ray which passes through the first focal point F 1 of a converging lens or proceeds toward the second focal point F 2 of a diverging lens is refracted parallel to the lens axis. IMAGE FORMATION BY LENSES There are three principal rays to locate an image. Ray 3. A ray through the geometrical center of a lens will not be deviated. Principal Rays A real image is always formed on the side of the lens opposite to the object. A virtual image will appear to be on the same side of the lens as the object. 23.7 a.Find the images formed by the following lenses using the Ray Tracing method. b. Write the characteristics of each image: -real or virtual, -larger, smaller or same size as object and -upright or erect. No image is formed. THE LENS EQUATION The lens equation can be used to locate the image: The ratio M is called the magnification, h o is the objects size and h i is the image size. Where d o is the objects distance, d i is the image distance and f is the focal length. R radius of curvature + converging- diverging f focal length + converging- diverging dodo object distance + real object didi image distance + real images - virtual images hoho object size+ if upright- if inverted hihi image size+ if upright- if inverted 23.8 A 5 cm tall object is located 30 cm from a convex lens of 10 cm focal length. a. Find the location and nature of the image. d o = 30 cm f = 10 cm = 15 cm, real b. What is the height of the image? h o = 5 cm = cm, inverted TOTAL INTERNAL REFLECTION The incident angle that causes the refracted ray to lie right along the boundary of the substance is unique to the substance and is known as critical angle of the substance. Total internal reflection Total internal reflection is the phenomenon that involves the reflection of all the incident light off the boundary. It only takes place when both of the following two conditions are met: - the light is in the more dense medium and approaching the less dense medium. - the angle of incidence is greater than the so- called critical angle. Critical Angle n 1 sin = n 2 sin = n 2 sin 90 sin = n 2 / n 1 An example of TIR is when a beam of laser light is directed into a coiled plastic. The plastic served as a "light pipe," directing the light through the coils until it finally exited out the opposite end. Once the light entered the plastic, it was in the more dense medium. Every time the light approached the plastic-air boundary, it was approaching at angles greater than the critical angle. The two conditions necessary for TIR were met, and all of the incident light at the plastic-air boundary stayed internal to the plastic and underwent reflection. Other examples of Total Internal ReflectionTotal Internal Reflection 23.9 Find the critical angle for an air-crown glass boundary. n i = 1.52 n r = 1 = 41 Dispersion in a Prism Light of frequencies closer to the natural frequency of the electron oscillators in a medium travels more slowly in the medium Since different frequencies of light travel at different speeds in transparent materials, they will refract differently and bend at different angles When light is bent twice at nonparallel boundaries, as in a prism, the seperation of the different colors is apparent Dispersion the separation of light into colors arranged according to their frequency Dispersion in a Prism Total Internal Reflection Critical Angle the minimum angle of incidence for which a light ray is totally reflected within a medium Total Internal Reflection the 100% reflection of light that strikes the boundary between two media at an angle greater than the critical angle Optical fibers utilize the concept of total internal reflection to feed light from one location to another, these cables are very useful for communications Summary so far ???Refraction Refraction is based on the idea that LIGHT is passing through one MEDIUM into another. The question is, WHAT HAPPENS? Suppose you are running on the beach with a certain velocity when you suddenly need to run into the water. What happens to your velocity? IT CHANGES! Refraction Fact #1: As light goes from one medium to another, the velocity CHANGES! Revision of the topic: Activity 5a: Plane Mirrors pg 61 Complete the activity at home Do it on a refill and submit at the start of the lesson Complete activity 5B Reflection of light: pg 67 at home on a refill. Activity 6a: pg 73 Refraction: complete. Refraction Suppose you decide to go spear fishing, but unfortunately you arent having much luck catching any fish. The cause of this is due to the fact that light BENDS when it reaches a new medium. The object is NOT directly in a straight line path, but rather its image appears that way. The actual object is on either side of the image you are viewing. Refraction Fact #2: As light goes from one medium to another, the path CHANGES! Refraction What EXACTLY is light doing when it reaches a new medium? We dont want you to think ALL of the light refracts. Some of the light REFLECTS off the boundary and some of the light REFRACTS through the boundary. Angle of incidence = Angle of Reflection Angle of Incidence > or < the Angle of refraction depending on the direction of the light Refraction Going from Air to Water The index of refraction, n, for air (vacumm) is equal to 1. The index of refraction for water is If you are going from a LOW n to a HIGH n, your speed DECREASES and the angle BENDS TOWARDS the normal Refraction Going from Water into Air The index of refraction, n, for air (vacumm) is equal to 1. The index of refraction for water is If you are going from a HIGH n to a LOW n, your speed INCREASES and the angle BENDS AWAY the normal Note: If the angles are EQUAL, then the n must be equal for each. The ray will pass straight through. Refraction Snells Law A scientist by the name of Snell discovered that the ratios of the indexs and the ratio of the sine of the angles are the same value! Example The refractive index of the gemstone, Aquamarine, is Suppose a ray of light strikes a horizontal boundary of the gemstone with an angle of incidence of 23 degrees from air. Calculate the SPEED of light in Aquamarine Calculate the angle of refraction within Aquamarine 1.90 x 10 8 m/s degrees Total Internal Reflection There is a special type of refraction that can occur ONLY when traveling from a HIGH n medium to a LOW n medium. Suppose we are traveling FROM water and going into air. Should the ANGLE OF INCIDENCE get TOO LARGE, the angle of refraction will EQUAL 90 DEGREES. We call this special angle of incidence the CRITICAL ANGLE, c, for that material (water in this case) Total Internal Reflection If we EXCEED the critical angle, for that material, the ray will reflect INTERNALLY within the material. We call this idea In this figure, the angle of incidence EXCEEDS the critical angle for water and the ray reflects according to the law of reflection at the boundary. The Critical Angle So the question is, how can you calculate the critical angle? Remember, it is when the refracted ray is equal to 90 degrees cc Example Suppose a light ray is traveling in heavy flint glass( n = 1.65) and once it strikes the boundary, enters air. Calculate the critical angle for flint glass degrees Lenses An application of refraction There are 2 basic types of lenses A converging lens (Convex) takes light rays and bring them to a point. A diverging lens (concave) takes light rays and spreads them outward. Converging (Convex) Lens Much like a mirror, lenses also take light rays from infinity and converge them to a specific point also called the FOCAL POINT, f. The difference, however, is that a lens does not have a center of curvature, C, but rather has a focal point on EACH side of the lens. Applications of Converging Lenses In figure A, we see an eye which converges what we see on the retina. In figure B, we see an eye which converges too LATE. The eye itself is often too short and results in the person being far sighted. In figure C, we see an eye which converges too SOON. The eye itself is often too long and results in the person being near sighted In the later 2 cases a Concave or convex lens is necessary to ensure the image is on the retina Applications of Converging Lenses A camera uses a lens to focus an image on photographic film. Ray Diagrams The rules for ray diagrams are the SAME for lenses as they were for mirrors except you go THROUGH the lens after refraction and instead of going through, C (center of curvature) you go through the actual center of the lens. ff Rule #1: Draw a ray, starting from the top of the object, parallel to the principal axis, then through f after refraction. Rule #2: Draw a ray, starting from the top of the object, through f, then parallel to the principal axis, after refraction. Rule #3: Draw a ray through the center of the lens. Lenses The Mirror/Lens Equation To CALCULATE the images position and characteristics you use the same equations you used for mirrors. An object is placed 35 cm in front of a converging lens with focal length of 20 cm. Calculate the images position relative to the lens as well as the images characteristics cm-1.33x This image is REAL (since the object distance is positive) and on the OTHER side of the lens. The image is INVERTED and ENLARGED. Lenses Formula used with Spherical mirror also apply to lenses Copy the Ex J pg 78 Txt bk Complete Activity 6D pg 79 qt 3 now. Rest for HW